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This document contains mathematical formulas and properties related to: - Arithmetic and geometric sequences - Trigonometric functions and their properties - Logarithmic and exponential functions - Derivatives of functions - Integrals and properties of integrals - Trigonometric identities

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paBeHCTBa: ao = l; am· an = am+n; am: an = am-n (amY=amn; (ab)n =anbn; (~J an a-n 1 ~ = lal ={a, ecJIH a ~ 0, -a,ecm1a <0 OcHOBHble CBOMCTBa MOAYfljt: la!~ O; lal-lbl ~ la ±bl~ !al+ lbl; I-al= la!; la-bj =lb-al. 1. Apu<jJMemu1JeCKaR. (~) (a, - nepBhIB 'IJleH, d - pa3HOCTb, n - '111CJIO 'IJieHOB, an- n-H 'IJieH, Sn - cyMMa n nepBhIX 'IJieHOB) an =a, +d(n-1); a11- I +an+Ia = . n 2 ' d a d =an - am ' (n ...,. m),·= n+I - an; ..,... n-m S = a1 +an ·n = 2a1 +d(n-1) ·n- n 2 2 ' an+am =ap+aq,rJJ,en+m=p+q. 2. I'eoMempu'leCKaR. (-:--:-) b1 - nepBhJH 'IJleH, bn - n-H 'lJieH (bn * 0), n- '!HCJlO 'IJieHOB, q- 3HaMettaTeJih ( q * 0 ), s,, - C)'MMa n nepBbIX 'IJieHOB bn=b1·qn-I; b;=bn-1.bn+I' bn*O; S __ bl (1-q") __ bl -bnq --~ IlpHq *l; n 1-q 1-q S11 =n ·b1npH q =1; q __ bn+I ,· n-m bnq =-· bn bm' b11bm =bpbq,rJJ,en+m= p+q Cy.M.Ma 6ecKoHe'lHOU zeoMempu1JeCKOU npozpeccuu S = _!!l__, lql< 1 1- q 06PA30BAHHE (a±b)2 = a2±2ab+b2; (a±b)3 = a3 ±3a2b+3ab2±b3 WIU (a±b) 3 = a3 ±b3 ±3ab(a±b); a 2 -b2 =(a-bXa+b); a 3 ±b 3 =(a±bXa 2 + ab+b2} (a±b±c) 2 =a2+b2+c2 ± ±2ab ±2ac + 2bc; (a±b) 2 =(a±bXa±b); (a-b) 2 =(b-a)2 flpOU3600Hble HeKomopbZX ¢YHKlfUU (a, b, k, C - nocmoRHHbte} , C' = O; (kx+b) = k; x' =1; (xn J=n·x"-1 ; (sin x)' =cos x; (cos x)' = - sin x; ( ) , 1 )' 1 tgx = - - ; (ctgx =--.-; cos2x sm2x ( ) , 1 , 1 lnx =-; (log0 x) =--; x x·lna (exJ=ex; (ax J= ax ·ln a; , 1 , 1 (arcsin x)= r:-7 ; (arccos x) = vl -x2 ~l-x2 ' ( , 1 , 1 arctg x) =- -2; (arcctg x) =- - - 1+ x l+x2 llpa6UJIQ ourj>rj>epem1upoeamm (u, v - rPYHKlJllll, c- nocmORHHGR) (Cv)' =Cv'; (u +v)' =u' + v'; ' (!!_v)' u'v - v'u(uv) = u'v +uv'; v2 (g(J(x)))' = g'(J(x))-J'(x), 2oe g(J(x))-CJZO:JICHCIJi rPYHKlJWI. TeoMempul/ecKuu CMblC!l npOU3BOOHOU f'(x0 ) = tg a =k 3tta'!eHHe IIpOHJBO,[l;HOii <i>YHJ<Uml B TO'IKe paimo yrJJOBOMY K03<t><t>mi:HeH'ry KacaTeJJbHOii K rpa<i>HKY cpyttKUHH B3TOii TO'll<e. <PU3U'leCKUU CMblCR npOU3600HOU v(t)= s'(t) CKOpOCTb - npOH3BO,[l;H3R OT KOOp,a:HH3Tbl IlO epeMeHH. a(t)= v'(t) y CKOpeHHe - npoll3BO,a:H3R OT CKOpocnt no epeMeHH. YpaeHenue KacamenbHOU Ypaetteu11e KacaTeJJbHOH K rpa<t>11Ky <i>YHKUH11 f e TO'!Ke rpa<t>11Ka c a6cuttccoii x0 y = J(xo)+ f'(xoXx-xo). )],JUI mo6hIX H3T)'pa.JihHhIX n 11 k, 6oJibllll1X 1, 11 mofihrx a ~ 0 11 b ~ 0 septthI paBeHCTBa: ef;;f; = ef;.efb,. (ef;} = W: Vf= ~ (b *o); w=:= ef;; Va= ef;i,. (Var =a; Va< efi;, ecJIH 0 ~a< b; 2ef;F=la!: 2n+r-;; = _2n+J; a_r;:. =Y,mEZ,nEN Ecm1 m<O, TO a>O, ecJrn m>O, TO a~O Ta6nu1Ja nepBoo6p03HblX HeKomopbtX PYHKIJllU (a, k, C - nocm011H11ble) <f>yHKIJ;IDI f(x) ITepsoo6pa3HaJI F(x) k kx + C x", (n E Z,n * -1) n+I _x_+C n+ 1 1 2,J";+C..fX SlDX -cosx +c cosx sinx + C 1 tgx+ C--- cos2 x 1 - ctgx + C- -- sin2 x 1 Inlxl+c- x ex ex+ cx ax ..E_ +C 1n a flpaBuna Haxo:J1Coe11UJ1 nepeoo6p03HblX: I . EcJIB F - nepBoo6p33H3R ,!IJIJI f, a G- nepsoo6p33HaR ,!IJIJI g, TO F + G eCTh nepeoo6p33H3R ,!IJIJI/ + g. 2. EcJJH F - aepBoo6p33H3R ,!IJIJI f, a k - nOCTOHHHaR, TO <i>YHKUHJI kF eCTb aepeoo6p33HaJI JJ.JU! kf 3. EcJIH F(x) - nepeoo6p33tta)[ ,!IJIJI ftx), a k *0 H b - noCTOHHHble, TO 1 - F(kx+b) ecTb nepsoo6pa3HaR k ,!IJIJIJ(kx + b). <PopMyna Hb10m0Ha - Jleu61-1u1Ja EcnH F- nepsoo6pa3Hfill .llllil/Ha [a;b], To b fJ(x) dx = F(b)- F(a) a HeKomopb1e cBoiicmBa uHme2pana b b fkf(x)dx =k_- ff(x)dx; a a b b b f(J(x)+g(x))dx= ff(x)dx+ fg(x)dx a a a
0cH06Hble </Jop.i1ynbl 2 2 2 1 7! sin x +cos x = l; 1+ tg x = --2 -, x =t - + nn, n E Z; cos x 2 . sin x 1! cos x tgx =-·-, x =t-+nn, n E Z; ctgx =-.-,x=t nn, n E Z; cosx 2 sm x nn 2 1 tgx·ctgx = 1, x =t-, n E Z; l+ctg x =-.-2 -, x =t nn, n E Z. 2 sm x <PopMyRbl CRO:J/CeHUJl sin (x ± y) = sin x cosy±cos x sin y; cos (x ± y) = cos x cosy+ sin x sin y; ( + ) tg x ± tg y 1! tg x_y = , x, y, x±y=t-+nn,neZ 1± tg xtg y 2 <PopMyRbl OJIJI KpamHblX y2J106 sin 2x = 2 sin x cos x; sin 3x = 3 sin x - 4 sin3 x; cos 2x = cos2 x-sin2 x = 2cos2 x-l = 1-2 sin2 x; cos3x=4cos3 x-3cosx; tg2x= 2 tg~ ,x=t 1! +nn,neZ 1-tg x 2 sin2 ~ 2 <PopMyRbl nonoeuHHOZO apzyMeHma 1- cos x 2 x 1+ cos x cos - 2 2 2 x sin x tg-=--- 2 1+cos x 1-cosx x =t 1! +2nn, n E Z sin x </JopMyRa OOnORHUmeRbHOZO y2lla a sin x + b cos x = ~a2 +b2 sin (x+rp), rlJ,.e rp =arctg~ a 3HGKU mpuzoHOMemput/eCKUX </JYHKlfUU sin a cos a tga H ctga arcsin(- x) = - arcsin x; arccos(- x) = ;r - arccos x; arctg(- x) = - arctg x; arcctg(- x) = ;r - arcctg x; arcsin x + arccos x = 1! npH !xi ::::; 1; arctg x + arcctg x = ,. ; 2 2 sin(arcsin x) = x rrpw lxl ::::; 1; cos(arccos x) = x, ec.JIB lxJ ::::; l; arcsin(sin x) = x rrpw !xi::::;!!_; arctg(tg x) = x npH I~< 1!; 2 2 arccos(cos x) = x npH 0::::; x::::; ;r; tg(arctg x) = x rrpw x ER; ctg(arcctg x) = x; arcctg(ctg x) = x, ecJilf 0 < x < ;r. ao oo 30° 45° 60° 90° 120° 135° 150° a' pa,11, 0 tr 16 tr 14 tr /3 tr /2 2 tr /3 3tr 14 5tr16 sin a 0 I Ii. .f3 I .f3 Ii. I - - - - - - 2 2 2 2 2 2 .f3 Ii. I I Ii. .f3cos a I - - - 0 -- - - - - 2 2 2 2 2 2 I .f3 -Ji 1 tga 0 .f3 1 - - 1 -J3 .f3 I I -Jictga - 1 J3 0 - .f3 - 1 180° tr 0 - 1 0 - <Pop,i1y.?bl npeo6pG306aHUR cyMMbl e npoU3eeoeHue . . 2 . x+y x-y smx+silly= Sill--cos--; 2 2 . . 2 . x-y x+ y Sill x - Silly= sm--cos--; 2 2 x+y x-y cos x +cosy= 2 cos--cos--; 2 2 2 . x+ y . x-y cos x - cosy=- sm--sill-- · 2 2 , sin(x±y) 1! tg x ± tg y = , x, y =t - + tm, n E Z; cosxcos y 2 sin (y±x) ctg x ± ctg y = . . , x, y =t nn, n E Z smxsmy </JopMyRbl npeo6pG30BGHUJl npoU3eeoeHUR 6 cyMMy sin x ·sin y =2-(cos(x- y)- cos(x + y )); 2 cos x ·cosy =2-(cos(x - y )+ cos(x + y )); 2 sin x ·cosy =2-(sin(x - y)+ sin(x+ y )) 2 YHu6epCGllbHG5l noocmaH06KG 1- tg 2 ( ~) . 2 tg(~) COSX= (x) ' s1n x = ( x)' 1+ tg2 - 1+ tg2 - 2 2 x =t 1! +2nn, n E Z <PopM)IRbt npueeoeHuJ! tr tr 3tr a tr-a tr+a --a -+a --a 2 2 2 sin a sin a - sin a cos a cos a - cos a cos a - cos a - cos a sin a - sin a - sin a tga - tga tga ctga - ctga ctga ctga - ctga ctga tga - tga tga 0 I Ii. .f3a - - - 2 2 2 arcsma 0 tr16 tr /4 tr /3 arccosa tr 12 tr /3 tr /4 tr 16 3tr -+a 2 - cos a sma - ctga - tga I tr 12 0 1 .f3a 0 .f3 1 arctga 0 tr 16 tr /4 tr /3 arcctga tr 12 tr /3 tr 14 tr16 270° 3 tr /2 360° 2tr sin(- x) = - sin x; ctg(- x) = - ctg x - 1 0 0 I - 0 0 - 11HcjJOpMa~•OHHO·cnpaao•Ha• ra6nu~a © 000•l1Hcjlonnacr•, 2007 r.Moc<aa, Kawupc<oe wocce,21 E-mail: mail@infoplast.ru Http://www.infoplast.ru 0 '° no.anucaHO 8ne.arb 09.02.09. Tupax 40003K3. 3aKa3 ~ 34555. 113,llarenb 000 •l1Hcjlonnacr•, MOCKBa, KawupcKoe wocce, 21. Ten./<PaKc: 8(495) 730·01·87. TunorpacP•• 000 •B•aa·Crap•. 107023. MOCKBa, yn. 3neKTµOJaBD,QCKa•. 20.
log0 b = c (r,11,e b>O, a>O, a 7= I) Tor,11,a H TOnbKO Tor,11,a, Kor,11,a ac= b. Oc11oe11oe 1w2apurj>Mu1JeCKOe moJ1Coecmeo alogab =b Ceoucmea Rozapurf>1110e (a> 0, a* 1, b > 0, c > 0) log0 l = O; lo~a = l; log0 (bc)= log0 b+log0 c; log0 ( %J=log0 b- log0 c; k log0 b =k ·log0 b; ecm1 k-qeTHoe: log0 bk=k·log0 lbl lo b = logcb (c 7= 1); ga logea log b=-1- (b7=l); a logba log nbk=!·log b a n a ax2 + bx + c = 0, a7= 0 D = b2 - 4ac - oucKpUMu11a11m Kea,n,paTHoro ypaettemrn. Ecm1 D < 0, To ypaettem1e He KMeeT .ueM:CTBJ1'TeJihHhIX KOpHeH. Ecnu D = 0, TO ypaeHem1e KMeeT 1 KopeHh b x=-- 2a Ecm1D > 0, TO ypaeHeH11e 11MeeT 2 KOplUI: - b+Ji5 -b-Ji5 XI= ' X2 = 2a 2a TeopeMa Buema Ecn11 rrpHBe.uettttoe KBa,n,parnoe ypaetteHlfe x2 + px + q = 0 KMeeT KOpHH Xi H X2 (T.e. D;::: 0), To X1 +X2 =-p, X1 ·X2 =q TeopeMa, 06pam11QJ! meopeMe Buema EcnH <rncna m 11 n TaKOBbJ, '!TO m + n =-p H m .n =q' TO JTH 'lHCna llBJllllOTCll x2+px+q=O. KOpID!MH ypaetteH11ll Keaopam11oe ypGfme11ue c 'lemHblM 6mOpbL111 K03rj>rf>ulfUeHmOM ax2 + 2kx + c = 0, 2oe b = 2k D*=k2-ac, (n*=±nJ * -k±.JD*Ecrrn D > 0, TO x1•2 = - - - - a k ecJIH D* = 0, To x = -- a PQ3J10:J1Ce11ue K6aopam11020 mpex1JJ1e11a Ha MHOJ/Cume.m Ecnu X1 If X2 - KOpHll KBa,n,paTHOro Ipex'l.netta a:l + bx + c, To a:?-bx - c = a(x - x J (x - x::) y=kx y=kx+b y = ax2 y =ax3 y=~ x ~ ~ __i1L; ---;r::o x y k < o/ . ___./ ~ o (........ x y = smx y y = cosx y y=tgx y = ctgx 2. 3. 4. • ecJll1 a < 0, TO peweIDlii HeT; • ecn11 a = 0, TO x =O; • ecm1 a > 0, TO x =±a. Ix - bl =a • ec1rn a < 0, TO perneHlfi1 HeT; • ecJIH a = 0, TO x =b; • ec1rn a > 0, TO x = ±a+b. ( 'I ( 'I [/(x) = g(x), If x,, =lg x,, <=> J(x)= -g(x} ![ /(x) = g(x), IJ(x~=g(x)<=> J(x)=-g(x), g(x);::: 0. • ecJrn b > 0, TO x = log0 b • ecm1 b ~ 0, TO pewem1i1 HeT y=ax 2. af(x)= bg(x)<=> J(x)· logca = g(x)· logcb, r.Qea > 0, a 7= 1, b > 0, b 7= I, c > 0, c 7= 1 B '1acm11ocmu, ypae11e11ue af(x)= ag(x)<=> J(x) = g(x) rx)}>O3. (u(x))f(x)= (u(x)f(x)<=> (u(x)) otl, J(x)= g(x) (npH a> 0, a 7= 1) 1. log0 f (x) = b <=>f (x) =ab 2. log0 f(x)= log0 g(x)<=> <=> ({/(x) =g(x), HnM {f(x) =g(x),J J(x)> 0. g(x)> 0. (J11H peuieHWI OaHH020 ypatmeHWl nepexoaam mo.1&1w >r odHaii 113 :)lflU:X cucme.v moii. KOmopall npo114eJ). I. 2. I. • • • • • 2. • • y (x-a)2 +(y-b)2 = R2 ~ ~ .[fW= g(x)<=> {f(x)= g 2 (x), g(x);::: 0 .fiW= M;'J <=> { f(x) = g(x), <=> J(x);::: 0 (11n11 g(x);::: o) sinx= a ecnH lal > I, TO peweHHii HeT; ecm1 lal ~ 1, TO X = (-lrarcsin a+trn, n E Z l..facm11b1e CJ1y1Jau: sin x = 1, x = tr +2m1, n E Z 2 sin x = 0, x =m1, n E Z sinx=-1 x=-~+2m1 nEZ , 2 ' cosx= a ecm1 lal > l, TO peweH11i1 1rnT; ecm1 lal ~ 1, TO x =± arccos a+ 2m1, n E Z L/acm11b1e cRyl./au: • cos x = 1, x =2m1, n E Z 7r • COS X = 0, X = - +ml, n E Z 2 • cosx=-1, x=tr+2m1,nEZ 3. tgx=a, x=arctga+ m1,nEZ 4. ctg x =a, x = arcctg a + m1, n E Z
KeaApaTHb1e HepaeeHCTea HepaeeHcTea c MOAyneM Jlorap111Q>M111"tecK111e HepaeeHCTBa (a* 0) (npHBOllllMbie K BHl1)' ax2 +bx+ c > 0, ax2 +bx+c2':0 , aX'+bx +c <O, ax2 +bx+cSO) fpa<j>HKOM <j>YHJG.lffl1 f(x) = al-+bx+c l!BnlleTCll napa6ona; KOOpt111HaTbl eepllll1Hbl b D Xo =--, Yo= f(xo)= -- 2a 4a ,Lilll peweRl1JI KBat(paTHOro HepaseHCTBa BbI<rnCnlllOT A11CKpHMHHaHT D H onpet1eilJl10T KOpHH KBat1paTRoro TPi!x•rneHa. • D<O 11 a>O HepaeettcTeo ax2 + bx + c > 0, ax2 + bx+ c :::0: 0 ax 2 + bx + c < 0, ax2 + bx+ c ~ 0 • D<011a<O HepaeeHCTBO ax'+ bx+ c > 0, ax 2 + bx + c z 0 ax 2 + bx+ c < 0, ax2 + bx+ c ~ 0 • D = 011a > O Hepaaettcrno ax 2 + bx+ c > 0 ax2 + bx+ c z 0 ax2 +bx+c<O ax2 + bx+ c ~ 0 • D=O 11 a < O HeoaeeHcTeo ax2 + bx+ c > 0 =2+ bx+ c z 0 ax2 + bx+ c < 0 =2+ bx+ c ~ 0 • D > 011a>O HepaaettcTeo ax2 + bx + c > 0 ax2+bx+c z 0 ax2+bx+c < O =2+ bx+ c ~ 0 • D>O 11 a<O Heoaeettcrno ax2 + bx+ c > 0 ax2 +bx+c < O ax2 + bx+ c ~ 0 OTBeT XER XE0 XER Xo 0TBeT XER XE0 X=X0 Xo ( " OrneT XE0 X =X0 XER I J x~2 x OrneT OrneT 1. 2. 3. 4. 5. x 2. 3. 4. 5. 2. 3. Ix-bl< a • ecn11 a s 0, TO perneHHH HeT; • ec1m a > 0, Tob-a<x<b+a Ix - bl 2: a • ec1m a s 0, TO x E R ; • ecmi a > 0, TO [ x:::O:b+a, xsb-a IJ(x) < g(x) <=> {f(x) < g(x), f(x)> -g(x) If(x) > g(x) <=> [f(x) > g(x), J(x)<-g(x) IJ(x) > lg(x) <=> f 2 (x)> g 2 (x) • ec.Tl11 a~ 0, TO pernemrn tteT; • ecJIB a > 0, TO 0 s x < a 2 /;>a • ecn11 a < 0, TO x :::0: O; • ecnn a = 0, TO x > O; • ec1m a > 0, TO x > a 2 { f(x):::o: 0, [.M < g(x)<=> g(x)> 0, f(x)< g 2 (x) { g(x):::o: 0, rrr::;. ( ) f(x) > g 2 (x); 1JJ -'-} > g x ¢:> { g(x)< 0, f(x):::o: 0 rrr::;. CC {f(x) > g(x), 1JJ-'-J>1JgXj¢:> () g x :::o:o • ecfill m s 0, a > 0, a *I, TO perneHHH HeT; • ecJm m > 0, 0<a<1, TO J(x) > loga m; • ecim m>O,a>I, TO J(x)<logam af(x)> m • ec1m m s 0, a > 0, a *I, TO XE D(f); • ecm1 m > 0, 0 < a < 1, TO f(x)<logam; • ecnH m > 0, a > l, TO f(x)>logam af(x)> ag(x) • ecirna> 1, TO f(x) > g (x); • ecnHO < a<l , TO J(x) < g (x) l. 2. (mER) log0 f(x) < m • ecJIB 0 <a< 1, TO f(x) >am; • ecn11 a > l, TO {f(x) < am' f(x)> 0 logaf(x) > m • ecim 0 <a< 1 TO {J(x)< am, ' J(x)> O; 3. 4. • ecfill a> 1, TO f(x) > am log0 f(x) > logag (x) • • ecsrnO<a < l, TO { / (x) < g(x), J(x)> O; ecilll a> 1, TO {f((x))> g(x), g x >0 logh(x)f(x) >log h(x)g(x) <=> l h(x)> 0, h(x)< 1, J(x)< g(x), <::> J(x)> O; l h(x)> 1, J(x)> g(x), g(x)> 0. l-Illcno nepeCTaHOBOK 113 n 3ilCMCHTOB P. =1·2-. ..-(n - l)·n=n! l{Hcno coqeram1ii 113 n 3neMeHTOB no m Cm= n! . Co=l n m!(n - m)!' n CeoiicTea coqeTaHHii Cm= Cn- m. Cm+Cm+I= Cm+I n n ' n n n+l l-Illcno pa3MCII.lCHHH 113 n 3JleMCHTOB no m Am= P ·Cm= __n_!_ n m n (n - m)! <l>opMyna 6HHoMa lliIOTOHa (a+br = c0 an+C1 an- lb+ ... n n C k n- kbk en bn...+ na +...+ n Hill1 ( b)n n n- lba+ =a +na +... n(n-1)...(n - k+l) n- kbk bn ...+ a +...+ k! I')J.C nEN H c;an- kbk = Tk+I CCTb (k + 1) - if 'IJICH B pa3JJOJKemrn 61rn0Ma (k = 0, 1, 2, ... , n) CyMMa 6HHoM11Han&RbJX K03<j>cl>mv1eHTOB pasHa 2n: c~ + c~ +... +c: = 2n '1HcjJopMaljHOHHO-Cnpaa04Ha5i ra6m14a © 000 •'1HcjJonnacr•, 2004 r. MocKea, KawHpcKoe wocce, 21 E-mail mail@infoplastru Http:l/www. infop/astru Ten.: (095) 320-94-89 0axc: (095) 320-94-88 ----- ·~--- 00 N 0 0
• 0 6 P A 3 0 8 A H V1 E l'fc. ) or ) _I ( ,,.,,; - - ' -f )( . - 'f ·) l ~www:1nfopl.ast.ru (f 6 - l/f?t) - (// ~O / - - ./ ~ .c....... ...... ..,,.........,...,,i.,. OnpeAeneHMe KOMnneKcHoro 'IMcna OnpeAeJleHMe1. LIVICJla BVIAa z=a+bi, rAe a VI b - AeiACTBVITeJlbHble 'iVICJla, i - MHV1Ma51 eAVIHVIUa, 6yAeM Ha3blBaTb KOMnneKCHb/MU. 0603HaYeHVle a= Rez, b=Im z. L!V1c11a z= a+ib VI z = a - ib Ha3blBatOT conpfl>K8HHb/Ml1. 3anVICb KOMnneKCHOro 'iVICJla B BVIA8 a+bi Ha3blBaeTC51 anre6pal1'18CKOU cjJopMoft KOMnlleKCHOro 'il/ICJla. LllllCJlO a 6yAeM Ha3BaTb JJ.8MCTBl1T8flbHOft '1aCTblO KOMnneKCHOrO 'iVICJla, bi - MHUMOU lfaCTb/O KOMnlleKCHOro 'iVICJla, b - K03cjJcjJ114ueHTOM npu MHUMOU l/aCTU. B03MO>KHbl cnyYaVI, KOrAa A8ritCTBVITeJlbHble 'iVICJla a VI b MOryT 6b1Tb paBHblMVI HYJllO. ECJlVI a= 0, TO KOMnJleKCHOe 'iVICJlO bi Ha3bl- aaeTC51 l/UCTO MHl1Mb/M. ECJlVI b= 0, TO KOMnJleKCHOe 'iVICJlO a+bi paBHO a VI Ha3blBaeTC51 JJ.8UCTBUT8flbHb/M. ECJlVI a=OVI b=OOAHOBpeMeHHO, TO KOM- nneKCHOe Y111c110 O+Oi pasHo Hy11t0. jJeftcraurenbHbte l/ucna /If l/11cro MH11- Mb1e '111cna npeJJ.cTaBnHIOT co6oft l/aCTHbte cny'1a11 KOMnneKCHoro l/11cna. Asa KOMnneKCHblX YV1c11a a+bi VI c+di yc11oa11111V1Cb CYVITaTb paBHbtMl1 TOrAa Ill TOJlbKO TOrAa, KOr,[a B OT,[8JlbHOCTVI paBHbl VIX ,[8lACTBVITellbHbl8 YaCTVI VI K03cpcpV1UVleHTbl npVI MHVIMOrlt 8,[l/IHVIUe, T. e. a+bi= c,+di, eCJlVI a=c VI b=d. 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ApryMeHTOM KOMnneKcHoro YV1c11a Ha3braaeTC51 yron cp, KOTOpbrrlt 06pa3yeT B8KTOP c noJlO>KVITeJlbHblM HanpasneHVleM OCVI a6CUVICC. Bellt.1'it.1HY yr11a <P MO>KHO HarltTVI c no- m a . b 3MOl.J.lblO '+'OPMYJl: cos<p = r VI Stn<p = r. Ta CVICTeMa VIMeeT 6eCYVICJ18HHOe MHO>K8CTBO pe- weHl/lrlt BVIAa cp+2nk, rAe k- 11to6oe uenoe YVIC- 110. TaKVIM o6pa30M, Jlto6oe KOMnJleKCHOe YVIC- 110 z VIMeeT 6eCKOH8'iHOe MHO>K8CTBO apryMeH- TOB, OTJlVIYalOl.J.IVIXC51 APYr OT p,pyra Ha 'iVICJlO, KpaTHOe 2TC. ECJlVI k= 0, TO Mbl nonyYVIM rllaB- HOe 3Ha'i8HVl8 apryMeHTa cp, KOTopoe VI 6yAeM Ha3blBaTb apryMeHTOM KOMnJleKCHoro 'iVIClla. ECJlVI B 3anVICb KOMnJleKCHoro 'iVICJla z BMeCTO a t.1 b nOACTaBVITb 3HaYeHVl51 a= rcoscp , b= rsincp , TO nonyYVIM HOBYIO cpopMy 3anV1CVI KOMnneKcHoro YV1c11a: z =r(coscp + isincp)I KOTOpa51 Ha3blBaeTC51 rpuroHOMeTp11'18CKOH cjJopMOH KOMnJleKCHoro 'iVICJla. npasMno nepexoAa or anre6paM'tecKoH ctJopMbl KOMnJleKCHoro 'tMCJ13 KTpMrOHOMeTpM'teCKOM: 1. 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Ec11V1 p,aHbl z1= r1(coscp1+ i sincp1) 111 z2 = r2 (coscp2 + i sin <p2 ), TO z1•z2= r1r, (cos(cp1+ cp2) +i sin(cp,+ cp,)); • C11o>KeHV1e KOMnlleKCHblX YVIC8Jl z,= a,+ib, VI z2= Cl1+ib2. z1+z2= a 1+ib1+a2+ib2= a1+a2+i(b1+b2); • Pa3HOCTb KOMnJleKCHblX YVICen z,= a,+ib, VI z2= a2+ib2. z,-z2= a1+ib,-a1- ib2= a,- a2+i (b,-b2); • YMHO>K8HVl8 KOMnJleKCHblX 'it.1C811 Z1Z2= a,a2-b1b,+i(b1a2+b2a) a1+ ib1 -- a 2 + ib2 = (a,a2+h1b2 ~+ i(~2b1- a1b2) ' (z2¢0) . a2+b2 nocneAOBaTenbHOCTM ECJlVI paccMOTpeTb P51A HarypaJlbHblX YVIC8Jl 1, 2, 3, ..., n, ... VI 3aMe- HVITb Ka>KAOe HaTypanbHOe 'iVICJlO n 8 3TOM P51AY HeKOTOPblM 'i~C­ llOM a., CJleAY51 HeKOTOPOMY 3aKOHy, TO Mbl nonyYVIM HOBblrlt P51A YVl- cen a 1, a1, ..., a._1, a01 ... , KpaTKoe o6o3HaYeH~e {a.} VI Ha3blBaeMblrlt 'iVICJlOBOrlt nocneAOBaTeJlbHOCTblO. OrpaHM'teHHbte noc11eAOBaTe11bHOCTM 1) OrpaHVIYeHHa51 caepxy, TO eCTb Cyl.J.leCTByeT B, TaK, YTO a,,sB, A1151 11to6oro nEN. 2) OrpaHVl'ieHHa51 CHVl3y, TO eCTb CY1.J.18CTBY8T A, TaK, YTO As b,,, AJ151 11t06oro nEN. ; 1 = r1r1[cos(cp1+cp2) + i sin(<p1+cp2)] , z" = r" (cos(ncp)+ i sin(ncp)); (n - 4e11oe YVICJlO) (ctJopMyna Myaspa). 2 n r .!. .. 'Pl(, cp+2kn . . cp +2kn)Ec11V1n - HaTypa11bH08YVICJlOVl z ¢0, TO v z =zn =v1z1lcos n + zsin n , rAe ~ - apV1cpMeTVl'i8CKVlrlt KOpeHb Vl3 nOJlO>KVITellbHOro 'iVICJla lzl, cp= arg z VI k=O, l , 2, ..., n-1 . 0 "l - 2kn . 2kn ,,~ 1 _ (2k+ l)n . l2k+ l)n ( _ . k-O )TM8TVIM, YTO vt - cos n +sin n, v-1 - cos n +srn n , n - L,2, ..., - , l , ..., n- 1. npeAenb1 nocneAoearenbHOCTM OnpeAeneHMe: YVICJlO a Ha3braaeTC51 npeAenoM 'iVICJlOBOrlt nocneAOBaTeJlbHOCTVI a., 8CJ1VI AJ151 Jlto6oro CKOJlb yrOAHO Manoro 'iVICna E> 0, Harlt- AeTC51 HaTypallbHblrlt HOMep N TaKorlt, YTO AJ151 acex YV1ce11 n?:.N Bb1no11H518TC51 MOAYllb pa3HOCTVI la.-al<E ~ V c>O3 N: V n?:.N=:> la,,-al<e. HaYVIHa51 c 3Toro HOMepa N ace YV1c11a 3TO~ nocne- AOBaTellbHOCTVI nonaAatOT 8 E OKpeCTHOCTb 'it.1C- 11a a. .QpyrVIMVI CJlOBaMt.1, HaYVIHa51 c HOMepa N BHe VIHTepaana a- e; a+e MO>KeT HaxOAVITbC51 He 6011ee KOHeYHoro 'iVICJla YJ18HOB nocnep,oaaTeJlbHOCTVI. lima,, =a 1r->oo TeopeMbl o npeAenax 'IMCnOBblX nocneAoearenbHOCTeH 3) OrpaHVIYeHHa51, TO ecTb cy~ecTayeT A, B, TaK, YTO Asa.s 8, AJ151 11t0- 6oro nEN, ~ cy~ecTayeT C>O, TaK, YTO la.l<C, AJ15111to6oro nEN. ECJl~ {a.} VI { b.} - AB8 CXOA51~~eC51 nOC118AOBaT8JlbHOCTt.1, TO: limc·an = c lim an= c·a , (c - 'i~CJlO); n~ n~ TeopeMa 0 npeAeJle CYMMbt: nycTb liman=a I limb,,= b ==!;> lim(a,, ±b,,) = liman + limbn= a+ b; MOHOTOHHbte nocneAOBaTeJlbHOCTM 1) so3pacTat01.J.1aH a.<a.-1, V nEN. 2) y6b1Bat01.J.1a51 a,,>a0 _ ., V nEN. 3) He B03pacTato~a51 a.>a•." V nEN. 4) He y6b1Bato~a51 a. sa•." VnEN. n-+«> 11 -+<:io n~ n~ n--+«i TeopeMa 0 npOM3BeAeHMe npeAenos: nycTb limall=a , limbll=b ==!;> lima,, ·bll = lima,, ·limb,, = a·b; 11-+<0 n-+<0 11-+oo JJ -+oo 11-.00 lima,, TeopeMa 0 npeAeJle 't3CTHOro: nycTb lima,,=a, limb,,=b, b¢0 ==!;> lim!£.bn = n~ n-+00 11-+«> n-t-oo ,, 11mb,, n-+OO a b' •
OnpeAeneewe npeAe.na xcno1oi lt>JBDIDI. DA110CTopo11111e npeAenllt. CaoicTBa npeiienos L11cno .4 Ha3olBaeTCSl 1pe,[1e1101.1 ¢>Y'r!KL.1H'1 _r-_Il.rl B TO'-iKe .T. ecn MAflSi lll060~ nOCfi8A0- 8aT811bHOCTM AOnyCTl1MblX 3HaYeHl1~ apryMeHTa Xn• (.t , ¢ Xo), CXO,[IS1ll!8~CS1 KXo 2) CYMMa KOHe'iHOro 'tMCfla 6.M. Yl1C8J1 eCTb 6.M. Yl1CJ10; 3) npe,Qe11 cyMMbl pa0eH cyMMe npe,Qenos Jim(/(x) + g(x)) = lim/(x) + lim g(x); x->xo x->.lo x-..t-0 (T.e. limxn=xo). noc11e,[I08aTeJlbHOCTb COOT88TCT8YIOll!l1X 3HaYeHll1C1 cpyHKL.1111111 /(x,,), n-+x 4) npe,Qen npo11130e,L1eH1115I paseH npo11130e,QeH11110 npe,Qe1100 lim/(x) ·lim/(x) = lim (J(x) ·g(x)) ;11 E N, CX0,[1111TCS1 K Yll1CJ1Y A, T.e. Jimf(x) =A. reoMeTpll1'-l6CKll1C1 CMblCJ1 npe,[lena 3TOC1 x~.to .t-+x0 x->.to x->xo cpyHKL.1111111, '-ITO,[11151 8C8X TOY8K X, AOCTaTOYHO 6111113Kll1X K TOYKe Xo, COOT88TCTBYIOll!ll18 3Ha'-leHll1S1 cpyHKL.1111111 KaK yrOAHO Mano OTJ1111YalOTC51 OT Yll1CJ1a A. 5) KOHCTaHTbl MO)KHO BblHOCll1Tb 3a 3HaK npe,L1e11a Jim c·f(x)= c·lim.f(x)' (c- Yll1C110); x->x0 .t->Xo f(x) Jim .f(x) 0AHOCTOPOHHHe npeAenbl. 6) lim = x-+xo ec11111 lim g(x) ?!O· Ct.t111raeTC5I, YTO x CTpeMll1TC51 KXo 11106blM cnoco6oM: OCTaBa51Cb M8HbWll1M, Y8M Xo (cnesa OT Xo). 60JlbWll1M, YeM Xo (cnpasa OT Xo). 111111i1 K011e611S1Cb OKOJlO TO'-IKll1 Xo. x-+xo g(x) lim g(x) ' x-+xo ' X4-Xo 7) ec111i1 Jim fix~ = 1, TO lim/(x) = limg(x) (/111 g Ha3blBalOTCS1 npe,Q811bHO 3K8!i1Ba-Y111cno A1 Ha3b10aeTcs:i npeAenoM ct>YHKl.IHH y f(x) cneBa B TOYKe ,t 0, ec11111A11S111106oro c<O CYll!6CTByeT Yll1C110 a=a(io)>OTaKoe, YTO np1i1 xE(xo-a;xo), BblnOJ1H518TCS1 Hepa- B8HCT80 l.f(x) - A1l<c, lim f(x)=A1 • X-+Xo- 0 x-.xo g X x.-.x0 x-+x0 118HTHblM!i1 np1i1 crpeMJ18Hll11i1 x KXo); npeAenoM ctJyHKl.IMM cnpaBa Ha3bl8a8TC51 8) 3aMeHa nepeMeHHoCl: nycTb ,QaHbl 03a111Moo6paTHb1e cpyHKL.11111i1 cp(x) 111 'l/J(x). Tor,Qa lim/(x)= lim /('V(t)). B YaCTHOCTll1 lim/(x) = lim/( 1 t);lim f (x) = Jim1(t 1 ). x-+x0 t-+cp(x0) x-+0 t-+oo x-+oo r-+0 'lfe>O, ::lcr=cr(e), 'If XE(x0 ;x0+cr) => lf(x) - A 2 i<s <=>Jim f(x)=A2x-+ x0+0 TeopeMa:.f(x)>g(x), B 0°(xo) 111 3 limf(x)=b 111 3 limg(x) = c. Tor,Qa b~c. CBOMCTBa npeAenoB. x-+x0 .r~x 0 np1i1 yCJ1081111i1, YTO np8,[1811bl lim f (x) Iii Jim g(x) CYll!8CTBYIOT 111 KOH8'-1Hbl: TeopeMa:/(x) < y(x) <g(x) 'if xE0°(x0) 111 3 lim/(x)= b 1i1 3 lim g(x)= b. x->.l'o .r-+x0.l'4-Xo .t-+.ro 1) ec111i1 npe,Qe11 Iimf(x)=a => f(x) =a+a. cpyHKL.111151 pasHa 3TOMY Yli1CJ1Y n1110c 6.M. Tor,[la limy(x) = b. x->xo lim/(x)=O <:::>'lfe>O, 3cr>O:lx- x0 l<cr => lf(x)-al<e, x->x0 HenpepblBHble li>YHKQHH HHX CBOMCTBa. lO'IKa pa3pb1Ba li>YHKQHM, KnaccH$MK3QHSI £ - CK011b yro,QHO Manoe Yli1CJ10, l.f(x)-al=a;.f(x)=a+a. • _ - 1 . sin x 1nepBblH aaMe'larenbHblH npeAen: 1m x = x-+0 nycTb cpyHKL.11i1S1 y-.f(x) Onp8,[18J18Ha B TOYK8 X0 111 8 He- KOTOpOC 0Kp8CTHOCTll1 3TOC1 TO'-IKll1. ¢yHKL.11i1S1 Y-'f(x) Ha3blBaeTCS1 HenpepblBHOill B TOYKe Xo, ecn1i1 CYll!8CTByer npeAen cpyHKL.1111111 B 3TOC1 TOY- Ke 111 OH paBeH 3HaY8Hli1IO cpyHKL.1111111 B 3TOill TOY- TO'IKH pa3pb1Ba Cl>YHKl.IMM - 3TOTOYKll1 B KOTOpblX Hapy- waeTC5l HenpepblBHOCTb cpyHKL.11i1111. TOYKa pa3pb1Ba Xo Ha3b1Ba8TC5l TOYKOC1 pa3pb1Ba 1 POAa cpyHKL.11i11i1 y f (x), ec111i1 B 3TOC1 TOYKe CYll!8CT8YIOT KO- H8l!Hble npe,[1811bl cpyHKL.1111111 CJleBa Iii cnpasa (OAHOCTO- POHHll18 npe,QeJlbl) lim f (x)=A, 111 lim f (x)=A2 . Bo3bMeM Kpyr pa,Q111yca 1, o6o3Ha'-1111M pa,L1111aHHY10 Mepy yr11a MOB '-lepe3 x nycTb O<X <n /2. Ha p111cyHKe IA.M l=sinx, ,Qyra 11B '-1111C- ··· 11eHHO pasHa 1..1eHTpa11bHOMY yrny X, IB C l= tgx. Tor,Qa s s s }. 1 1 !>MOB < ceKmopa MOB < 6.COB, 2 Slll X < 2 X < 2 tgx · Pa3,Qe11111M see Ha 2 1sinx > O 111 no11yt.t111M: 1< .x < 1 . Sill x cos x I COS X < Sl~ X < 1. T.K. limcosx= 1, TOno npll13HaKy CYll!BCTBOBaHli1S1 npeAe11os X->0 . C118AY8T lim Sl~ x = l . X-+0 c M O cosx A B a Jim ~ = 0 (aER, b>l); X-++oo b lim !In= I· '11-++co tan l lim 1 n = 1. 11-+00 -n Ke: lim/(x ) = f(x0) . x->."o 3ro 03Hat.taeT: • cpyHKL.11i151 onpeAeJleHa B TOYKe Xo 111 B ee OKpe- CTHOCTll1; • cpyHKL.11i1S1 111Meer npe,Qen np111 x-x0; • npe,[1811 cpyHKL.1111111 B TOYKe Xo paBeH 3Ha'-18Hli1IO cpyHKL.1111111 B 3TOC1 TOYKe, T.e. BblnOJ1HS18TCS1 pa- B8HCT80. 3TO 03HaYaeT, '-ITO np111 HaXO)K,[18Hli1111 npe,Qena HenpepblBHO~ cpyHKL.11111i1 f (x) MO)KHO nepeC1Tll1 K npe,Qeny nOA 3HaKOM cpyHKL.1111111, TO eCTb B cpyHK- L.lli1111 .f(x) BMBCTO apryMeHTa x nO,[ICTa- Bli!Tb npe,[1811bHOe 3HaY8Hll18 Xo. • X-+Xo-0 X-+Xo+O np111 3TOM, ecn111: • A1=A2TO TOYKa Xo Ha3blBaeTCS1 TO'-IKOl-1 ycTpaH!ilMOro pa3pb1sa; • A1¢ A2TOTOYKa Xo Ha3blBaeTC5l TOYKOC1 KOH8'-IHOro pa3- pb1Ba. IA1-A2I Ha3b1saercs:i cKaYKOM cpyHKL.1111111. TO'-!Ka pa3pb1Ba Xo Ha3b1Ba8TCS1 TO'-IKOl-1 pa3Qb1Ba 2 pona cpyHKL.11111i1 y f(x), ec11111 no Kpail!Heill Mepe OA111H 1113 O,[IHO- CTOPOHHll1X npeABJlOB (cnesa 111Jlli1 cnpasa) He CYll.8CTBY- er, 111i160 paseH 6eCKOH8YHOCTll1. • Jt' • -! .... 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Co6cTBelfHble senopbt nMHei4eoro oaeparopa M111:x csoicrsa I ECJ1V1 B 6a3.1C6 e Jl.1H61i1Hbllil onepaTOp .1M69T MaTpHLY .-1, a B 6a3.1C6 { e) onepaTop HMeeT MaTPVll.Y B, ~ det(A- A.E)= det(B- A.£), A. - npOV13BO!lbHOe Y1t1cno ;o! 0, E - 9AV1HV1YHafl MaTp1i11..1a. det(B-A.E) =det(T-1AT-A.T-'ET)= =det(T-' (A - A.E)T)= det r -1 det(A+A.X); detT=detA- 1 = delA 1 0 ... 0 a11-A. a12 ... a1,, az1 az2-A ..· az,, ... a,,1 a,,2... a,,,, 0 0 ... 1 ECJlV1 xapaKTepV1CTV1Y6CKV1 MHOrOYneH J1 V1H6i:1Horo onepaTopa np1t1pOBHSlTb K O, nonyYVIM xapaKTep1t1cT1t1YecKoe ypasHeH1t1e Jl1t1Hei:1Horo onepaTopa. Co6cTeeHHbte eeKTOpbt JlMHeMHoro onepaTcipa HeHynesolil BBKTOP xHa3blBa6TCSl co6CTB6HHblM BBKTOPOM JlV1HelilHoro onepaTopa, ecn1i1 AX=k X onepaTop K x, nonyY1t1M 3TOT )!(9 x, yMH0- )!(6HHbli:i Ha HeKOTopoe k. k - co6cTBeHHoe Y1t1cno onepaTopa A=(; ~) -+ (2 1] ( I) l ll -+ Ax = 3 0)' - 3 = (- l)·c-3)= - x 12. noeepxHOCTM eroporo nopRAKa OnpeAeneHMe:YpasHeH1i1e B1t1Aa a11x2 +2a,2xy+2a22y2 +2auxz+2a23yz+a33 z 2 +2a14x+2ai4y+2a31 z+a44 =0, rAe aij(i,j = 1...11) A6t1CTBV1T6J1bHble 'iVICJla, Ha3blBaeTCSl 06ll.1"1M ypaBH6Hlt1- eM nosepxHOCTV1 BToporo nopRAKa. B 3aBl-1CV1MOCT"1 OT napaMeTpa a~ nonyYalOTCSl CJ16AYIOll.IV16 KJ1aCCV1Y6- CKV1e noaepXHOCTV1 (BCe napaMeTpbl nOJ10)t(lt1T6JlbHbl6 Ylt1CJ1a): 2 y2 z2 x2 +-b2 +1=1- rpexocHblM :Jnnuncou,a; a c x2 y 2 z2 ~+ -b2 -2=1- o,aHononocHblM runep6onou,a; a c 2 y2 z2 x2 +-b2 -2 =-1 -,asynonocTHblM r11nep6ono11,a; a c 2 y2 z2 x, +-b2 -2=0 - KoHyc sroporo nopHfJ.Ka; a- c 2 2 ; 2 +}i-= 2z - ann11nr111./eCK11i1 napa6ono11.a; 2 2 ; 2 - ~2 = 2z - r11nep6onu'leCKMM napa6onou/l,; x 2 +y 2 +z 2 =0 - TOl./KM. 2 2 ?+ti-=1 - 3flfll1nTl11./8CKUM L/MflMH/l,p,' x2 y2 a2- b2= I - r11nep6on111./ecK11i1 qun11H,ap; q2 =2ax - napa6onul./eCKl1MLJMflUH/l,p; a2 x2 - b2 y2 =0- napa nepeceKa10~11xcH nnocKocreill; x2 - a2 = 0 - napa napannenbHblX nnocKocreu; x2 +y2 = 0 - npHMaH. Bee yKa3aHHble ypasHeH1t1fl Ha3b1Ba10TCfl KaHOH1t1YecK1t1M1-1. OCHOBHblM M6TOAOM V13YY6Hlt1Sl nosepXHOCTelil BToporo nopS!gKa - M6TOA ceYeHVllil, KOTOpbllil COCTOVIT B nocTpoeHV1V1 J1V1HV1iil (CeY6HV1i:i) gaHHblX nllOCKOCTelil B YaCTHOCTV1 c nnocKOCTSlMV1, napannenbHblMV1 KOOPAlt1HaT- HblM nnOCKOCT51M. 10. fiJJOCKOCTb BnpDCTpaHCTBe. BMAbl ypaseeHMA nnoc1oc1ei4. Vron MeJKAy nnocKOCTAMM YpaeHeHMe nnocKOCTM, npoxoAHIJ.leM 'fepe3 33A3HHYtO TO'fKy, nepneHAMKYllHPHO A3HHOMY eeKTOPY nycTb nllOCKOCTb 3agaHa TOYKOlil M0 (x0 ;y0;z0) V1 BeKTO- pOM n(A;B;C)' nepneHAl-1KYllflPHOlil 3TOVI nJlOCKOCTl-1. 803bM9M npOl-13BOJlbHYIO TO'iKY M(x;y; z) 1-1 COCTaBl-1M B9KTOp M0M., = (x-x0 ; y-y0; z-z0). np1-1 Jll060M pacno- Jl0)!(8HV1V1 TOYKl-1 M Ha nJlOCKOCTl-1 Q rtJ_ MoM . n03TO- MY ti·M0M = 0. A (x-x0)+B(y-y0)+C(z-z0)=0 0611.1ee ypaeHeHMe nJlOCKOCTM 6.: Ax+By+Cz+D=O • Ecn1-1 D=O, TO gaHHOMY ypaBHeH1t110 YAOBneTsopReT TOYKa 0(0;0;0). • ECJll-1 C=OTO BSKTOp n(A;B;O).loz. CJ18AOBaTeJlbHO, nnOCKOCTb napanJlSJlbHa OCV1 oz, ec111-1 B=O - TO oy, 6CJ1V1 A= 0 - TO ox. • ECJ1V1 C=D=O, TO nnOCKOCTb npOXOAl-1T Yepe3 0(0;O;0), napannenbHO oc1.1 oz. AHanor1t1YHO np1-1 A=D=O1-1 B=D=O. • ECJll-1 A=B=O, TO ypaBH6HV1e npL'1M6T BL'1A Z=-@ nnocKOCTb napannenbHa nnocKocr 1i1 OxJ'· • ECJ1V1 A=B=D=O, TO ypaBH6HV1e l-1M66T BL'1)J, z=O. 3To ypaBHeH1t1e nnocKOCTV1 Oxy . YpaeHeHMe nnocKOCTM, npoxoAHIJ.leM 'fepe3 TPM TO'fKM 803bMeM Ha nllOCKOCTV1 TOYKY P(x;y;z). CocTaB1t1M seKTOpb1: ---+ KP=(x- x,; y-y,; z- z1) KM=(x2-x,; y2-y,; z2-z1) KJi!=~r.3-x1; y3-y,; Z3- z,) 3TV1 B9KTOpbl Jle)t(aT B OP,HOi:i nJlOCKOCTV1, cnegoBaTe!lb- HO OHV1 KOMnJlaHapHbl: y - y, z- z1 ) 12-Y1 Z2- Z1 = 0 Y3-Y1 Z3-Z1 YpaeHeHMe nnocKOCTM e oTpe3Kax nycTb nllOCKOCTb OTCeKaeT Ha OCSlX OTp93KV1, T.e. npoXOAVIT Yepe3 TOYK"1: A(a;O;O) B(O;b;O) C(O;O;c) x- a y z x y z 1 - a b 0 = 0 - +-b +-=a c -a 0 c HopManbHOe ypaeHeHMe nnocKOCTM Id= Ix.cosa. +y .cos p+ z .cosy - p 11 "1HcpOpMa1.4HOHHO-cnpaBOYHaS1 Ta6nH1.4a I • © 000 «V1Hc:j:lon11acT», 2006 •I . . r. MocKsa, Kaw1-1pcKoe wocce, 21 -• • E-mail: mail@infoplast.ru, --• http://www.infoplast.ru •• •Ten.: (095) 320-94-89/88 ' Cl C• ~ LI'.... ='() "°'-...... ~ LI' : '() •......: '() •o ;,,._ 0 '() (t, -~ no.anHCaHO s ne'ISTb 30.03.06. THp8)K 4000 3K3. 3aKa3 N!/3106. "13.Qarenb 000 «"1H¢onnacr», MocKsa, KawupcKoe wocce, 21. Twnorpa¢Hfl 000 •Busa-Crap». 107023, MocKsa, yn. 3fleKTfJ038BO.O.CKaR, 20.
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Cnosa, o603Ha4al0Ujll1e KO!lll14eCTBO, CTO- HT nepeA cylljeCTBll1Te!lbHblM . ,Qm1 MC'lMCnSleMblX cy14ecTBMTenbHblX: 0A111H One table Kall<AblH each/every table ,[lsa/o6a/napa two/both/a couple of tables Tp111 111 T.A. three etc. tables HecKO!lbKO a few/several tables MHoro Mano many/a number of tables few tables ,QnSI HeMC'lMCnSleMblX cy14ecTBMTenbHblX: HeMHoro a little sugar MHoro much sugar OYeHb MHOro a great deal of sugar Mano little sugar ,QnSI MC'lMCnSleMblX .. HeMC'lMCnSleMblX cy14eCTBMTenbHblX: HeT no tables, HeMHoro some sugar tables, sugar(HeKOTOpoe KO!lll14eCTBO) MHoro a Jot of/Jots of tables, !plenty of sugar 5onbwaH YaCTb most tables/sugar Bce/ secb 8HMM8HMe! Few - Mano Little - Mano all tables/sugar a few - HeMHOro (HeCKOflb- KO WTYK) a little - HeMHoro (HeKOTO- poe KOflll14eCTBO MHo>KeCTBeHHOe '!Meno cy14ecTBMTenbHblX 50!lbWll1HCTBO c ylljeCTBll1Te!lbHblX o6pa3y- e T MHOll<eCTBeHHOe 4111Cfl0 c nOMOUjblO OKOH- 4 a Hll1H -S. E c 11111 eA111HCTBeHHOe Y111c110 0 KaHY1110aeTCH Ha: S, sh, ch. X, z - np1116a0m:1eTCH OKOHYaHHe -es: classes, bushes, ditches. minxes. buzzes. 0 - np1116aa11HeTC5! OKOtNaM1e -s. es. ooiatoes. eroes. rnaCHblH + y - np1116aB11HeTCH OKOHYaH111e -s: toys, bays cornaCHblH + y , - y MeHHeTCH Hai 111 npH6aB- !1HeTCH OKOHYaH111e -es: babies, parties. BHMM8HMe! HCKfllO'leHMSI: EA.'!. MH.'l. Child children Foot feet Louse lice Man men Mouse mice Ox oxen Sheep sheep Tooth teeth Woman women HeKOTOpb1e cnosa Heattrn111HCKoro npo111c- XOll<AeHHH 111MelOT 3all1MCTBOBaHHble cpopMbl MHOll<eCTBeHHOro 4111CJla: EA.'!. MH.'l. Analysis analyses Appendix appendices, appendixes Bacterium bacteria Basis bases Crisis crises Criterion criteria Curriculum curricula Datum data Medium media Memorandum memoranda Oasis oases Phenomenon phenomena Stimulus stimuli Syllabus syllabuses, syllabi Vertebra vertebrae np11TS1>1<aTenbHb1iil naAe>K y aHrnll1HCKll1X cylljeCTBll1Te!lbHblX scero ABa n~ell<a - 061411iil 11 npMTSl>KaTenbHblM. np111rnll<aTeflbHblH naAelK 06pa3yeTCH C noMOll.blO OKOHYaH111H - 's AflH eA111HCTBeHHoro 4111C!la 111 -s' AflH MHOll<eCTBeHHOro. The boy's book Ho: The boys' books. Ec11111 CylljeCTBll1Te!lbHOe OKaH4111BaeTCH Ha s , TO B03M0)1(Hbl o6a 0ap111aHTa OKOHYaH111H: James's bag 111111 James' bag. ApntKllb OnpeAeneHHblM a pTMKnb (THE) OnpeAeneHHblH aprnKflb ynoTpe611HeTcH: - c 111C4111C!lHeMblMll1 cylljeCTBll1Te!lbHblMll1 B eA111HCTBeHHOM 111 MHOll<eCTBeHHOM 4HC!le, - C Hell1C4111C!lHeMblMll1 CylljeCTBHTe!lbHblMll1. THE ynoTpe6nS1eTCS1: - ec11111 npeAMeT H3BecTeH ro0opH1.4eMy: "'ie car I have s very 'ast ~e e who ere ay '19 'oott:Ja e - Ec11111 npeAMeT ynoM111Ha11cH paHee: Mary drank a glass of wine. Then she washed the glass and put it away. - EcnH npeAMeT eA111HCTBeHHblH B CBOeM po- Ae: The sky is blue. The sun is shining. - Ec11111 cylljeCTB111Te!lbHoe B eA111HCTBeHHOM 4111c11e npeACTaBnHeT 4e11b1H Knacc npeA- MeTOB: The average family now has a computer. The computer is a most important invention. - Ec11111 nepeA cylljeCTBll1TeflbHblM CT0111T np111- 11araTe!lbHOe B npeBOCXOAHOH CTeneH111: Theresa is the tallest girl in town. HeonpeAe n e HHblM apTMKflb (A/AN) HeonpeAeneHHblH aprnKflb ynoTpe611HeT- CH TO!lbKO c 111C4111C!lHeMblMll1 cylljeCTBll1Te!lb- HblMll1 B eA111HCTBeHHOM 4111Cne: a boy, a spring, a dictionary, a piece of chalk. CllopMa AN cTaB111TcH nepeA cylljecrn111- Te11bHb1M111, Ha4111Hal0Ujll1Mll1CH Ha rnaCHblH: an apple, an examination , an hour (Ho a universi- ty, a hotel). A/AN yno Tpe611S1eTCS1: - Ec11111 npeAMeT He11130ecrnH rosopHUjeMy: I have a car. Mary has a test tomorrow. - Ec11111 npeAMeT ynoM111HaeTcH 0nep0b1e: A banana is usually sweet. A book is a good friend on a long trip. OTCYTCTBMe apTMKflSI nepeA 111C4111C!lHeMblMll1 CylljeCTBll1TeflbHbl- Mll1 BO MHOll<eCTBeHHOM 4111C!le 111 Hell1C4111C!lHe- MblMll1 CylljeCTBll1Te!lbHblMll1 He CTaBll1TCH onpe- Ae!leHHblH apT111Kflb, KOrAa OHll1 o603 Ha4alOT secb Knacc npeAMeTOB. I like cherries. The cherries in this bag are ripe. Chinese grow rice. The rice I ate last night was good. BHMM8HMe! nepeA cylljeCTBll1Te!lbHblM B eA111HCTBeHHOM 4111C!le 06H3aTe!lbHO AO!lll<Hbl CTOHTb: - aprnK!lb (a book, the car, an uncle) 11111111 - yKa3aTenbHOe Mecrn111MeH111e (this TV, that radio, this book) 11111111 - np111rnll<aTe!lbHOe MeCTOll1MeH111e 11111111 c yllje- CTBll1Te!lbHOe B np111rnll<aTe!lbHOM naAell<e (my pencil, her key, Mary's room). MecT01r1MeH1r1ff n1114Hble MeCT0111MeHll1H 111MelOT AB8 naAe>Ka: 111MeHll1Te!lbHblH 111 06beKTHblH . "1MeH11Te11bHblM naAe>K (c11y>1<11T n0Ane>1<a1411M) I >1 You He, she, it We You They Tb / OH, OHa, OHO Mb / Bbl OHM BHM aHtte! ecT0111 eH111e you acerAa Tpe6y- e~ - aro a a cpopue o ecrne >;Oro Yl-!Cna.
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I like to drive myself. - 51 111061110 secT111 Maw1-1- HY caM. 6e3/1M"IHble MeCTOMMeHMSI One (s 3Ha4eHHH «mo6oc; 4e11oseK», «1110AH» B 4e110M) One should always be on time. You (s 3Ha4eHHH «111060H 4e11oseK», «1110AH» B 4e110M) I am lost: how do you get to the train station from here? They (B 3Ha4eHHH «HeKTO», «1110AH» B 4e110M. They say the weather will be warm in summer. - rosopsiT, 11ernM 6yAeT Ten110. . lllMfl np1,u1araTenbHoe np1-111araTe11bHble B aHf!lHHCKOM Sl3b1Ke CTOSIT nepeA onpeAe11SleMblM C110BOM. CTeneHM cpaeHeHMSI np11111araTe11bHblX. 0AHOC110:>t<Hb1e 1-1 ABYXC~O:>t<Hb1e np1-111araTe11b- Hb1e o6pa3ylOT CTeneHH cpaBHeHHSI c noMO- LlblO cycpcpMKCOB: - cpaBHMTe/lbHSSI CTeneHb: -er - npeBOCXOAH8SI CTeneHb: -est big - bigger - biggest; clever - cleverer - cleverest np11111araTe11bHble 6011ee 4eM 1-13 ABYX C110rDB- C nOMOLLblO C110B: - more - cpaeHMTe/lbHasi cTeneHb - the most - npeBOCXOAH8SI CTeneHb Beautiful - more beau ifu1 - the most bea Extravagan - ore exrravaga e mos extra ag L BH111MaH111e: nepeA np1-111araTe11bHblM B npe- BOCXOAHOH CTeneHH BCerAa CTOHT onpeAe- 11eHHblH aprnK11b. Earth is big. Uranus is bigger. Jupiter is the biggest of all planets. Nuclear physics is the most difficult subject of all. nocK011bKY aHmHHCKMe cyl.leCTBHTe11b- Hb1e He CK110HSllOTCS'I no nSAe:>KaM, cpyHK4MH nSAe:>KeH 6epyT Ha ce6si npeA11or111. npeA/lOr - 3TO c11y>1<e6H8SI "18CTb pe"IM, nOK83blB8IOll.l8SI cne4111cp1111.1ecKMe OTHOWe- HMSI Me>KAY ABYMSI npeAMeTSMM. Cyl.leCTBMTe11bHb1e c npeA110raM1-1 OTBe4alOT Ha BOnpOCbl «fAe?», «KOfAa?», «KaK?», a TaK>Ke Ha naAe>KHble BOnpOCbl. The boys are in the yard («r!Je?») Mary is coming by train («KaK? ») We leave at5.00 p.m. («KOr!JB? ») I gave the book to my brother («KoMy? ») The children are drawing on the pavement («Ha YeM? ») with chalk («YeM? ») Ha1116011ee ynoTpe6111Te11bHb1e npeA11or111 about above across after against along among around at before behind below beneath beside between beyond by despite down during for Ill MX OCHOBHble 3H8"1eHMSI: o; BOKpyr HaA nonepeK; HanpoTMB noc11e nporns BA011b cpeAH BOKpyr y, OK0110 nepeA 3a nOA noA OK0110 Me>KAY noA; 3a y, npH, OK0110 HeCMOTpSI Ha BHM3 BO BpeMSI A11S1 from oT, 1113 in(tb} B like C110BHO near so311e Of OT off yKa3blBaeT Ha OTAMeHHe OT 4ero-11. on Ha out 1113 (OTAa11eHHe, ABH:>KeHHe Hapy:>t<y) over through throughout till to(ward)(s) under HaA CKB03b (Ha)CKB03b AO (speMs:i) K (Hanpas11eH1-1e) noA until up upon AO (speMsi) yKa3blBaeT Ha ABM>KeHHe BBepx Ha with within without c B (npeAe11ax) 6e3 BHMM8HMe! Ka:>KAblH aHf!lMHCKHH npeA110f HMeeT HeCK011bKO (11111111 MHOro) 3Ha4eHHH Ill c11y4aes ynoTpe611eH111s:i. Ha aonpocb1 Koro? Yero? KoMy? YeMY? 0 OrneYalOr cy~. c npe!JI10fBM/lf of, from to with HapeY111e MHorne Hape4HSI o6pa3ylOTCSI OT np1-111a- raTe11bHblX c nOMOLLblO cycpcpMKCa -ly (quick- ly, naturally, beautifully, largely etc.). He spoke quickly (quick+ly) She opened the box very carefully (careful+ly). Hape"IMSI "18CTO OTBe"ISIOT HS eonpOCbl: KaK? She opens the present quickly. rAe? She opens the present inside. KorAa? She opened the present yesterday. B KSKOM cTeneH111? She opened the present very quickly. Hape"IMSI MOryT 03H8"18Tb: - speMs:i (tomorrow, yesterday, today, early, late, etc.) John arrives tomorrow - 4aCTOTY cosepweHMSI AeHCTBHSI (some- times, usually, often, never etc.). How often do you smoke? - I never smoke. 100% < = > 50% => <=> 0% always usually sometimes rarely never often occasionally seldom hardly ever not ever Hape4HSI, o603Ha4al0LlHe speMs:i CTOSIT B Ha- 4a11e 1-111111 B KOH4e npeAf10>KeHHSI. I saw my friend yesterday. Tomorrow we shall go to the library. Hape41-1si, o6o3Ha4al0LlHe 4acT0Ty cosepwe- HHSI AeHCTBMSI, CTOSIT - nepeA maro110M B npocTblX speMeHax: usu- ally comes, never ate, often do, never had She usually comes at 8 p.m. - noc11e maro11a to be B npocTblX speMeHax: is usually, are never, was often, were rarely She is usually on time. Me>KAY BCnOMOraTe11bHblM HOCHOBHblM maro- 110M B c11o:>t<Hb1x speMeHax: has always been, will never eat, had often come. She has always been on time. CTeneHM cpaeHeHMSI Hape1.1Mi4 Hape4111si 06pa3y10T cTeneHH cpasHeHMSI TaK >Ke, KaK np1-111araTe11bHb1e. Hape4HSI Me- Hee 4eM H3 ABYX c11oros - c noMOLLblO cycpcp1-1- Kcos: -er (cpaBHHTe11bHasi crnneHb) -est (npesocxOAHasi crnneHb) late - later - latest early - earlier - earliest. Hape4HSI, COCTOSILLHe 6011ee 4eM 1-13 ABYX C110rDB, a TaK>Ke 6011bWHHCTBO Hape4HH Ha - ly, o6pa30BaHHblX OT np1-111araTe11bHblX, - c noMOLLblO C110B: - more (cpaBHHTe11bHas:i cTeneHb) - most (npeBOCXOAHas:i CTeneHb) quickly - more quickly - most quickly intensely - more intensely - most intensely BHMM8HMe! lllCK/llO"leHMSI: Well - better - best Badly - worse - worst Much - more - most Little - less - least /lfH¢opMaljJ10HHO-cnpaao4HilR ra6nuqa C 000 •/lfH¢onnacr•,2004 r MocKBll, KawHpcKoe wocce, 21 E- ma&111/oplastIU ....,..n/oplast.IU
HH4'0nlACT ™ www.infoplast.ru AHrmticKMi rnaron <l>opMbl, epeMeHa, 3anorn AHrm1i;CKi.1i; rnaron i.'!MeeT Tpi.1 OCHOBHblX cpopMbl: 1 - HeonpeAelleHHaJI <1>opMa 2 - npoWeAWee BpeMSI 3 - np11'iaCTlle npoweAWero epeMeHll (np11'iacT11e II) 2 3 Stay stayed stayed Want wanted wanted Look looked looked Study studied studied npae1-111bHb1e rnaro11b1 o6pa3ytoT eTopyto "' TpeTbto cpopMbl c noMOl.11bto cycpcp1-1Kca -ed. 50J1bWi.1HCTBO aHrni.'li;CKi.'IX rnaronoe npaBi.'!Jlb- Hble. YeTeeprnR cpopMa rnarona 06pa3yeTCR c no- MOl.11bto cycpcpi.1KCa -ing («i.1HroBaR» cpopMa) «111HroeaR» cpopMa MO:>KeT RBJlRTbCR: - np1-14acrneM HaCTORl.11ero epeMeHi.1 (np1-1- 4acrneM I) · - repyHAi.'leM. np1-14acrne HaCTORl.11ero epeMeHi.1 CllY:>Ki.'IT B npeAJlO)l(eHi.'li.1 onpeAeJleHi.'leM: a playing boy, a rolling stone, a dancing girl. EAi.1Hi.14HOe np1-14acrne CTOi.'IT nepeA onpeAe- JlReMblM CJlOBOM. np1-14acrne, BXOARl.11ee B np1-1YaCTHb1i; o6opoT, CTOi.'IT nocne onpeAellR- eMoro cnoea: a boy playing football, a stone rolling down, a girl dancing salsa. fepyHAi.'li; BblnOJlHReT T8 :>Ke cpyHK4i.1i.1, 4TO i.1 cy1.11ecTBi.1T8JlbHOe. Walking is a good exercise (nOAJ1e:>Ka1.11ee). We enjoy playing tennis (Aono11HeH1-1e). B Ka4eCTee AOno11HeHi.1R repyHAi.'li; ynoTpe6- JlReTcR nocne onpeAeJleHHblX rnaronoe: Appreciate Avoid Consider (think aboulj Discuss (talk aboulj Enjoy Finish (get through) Keep (keep on) Quit(give up) Suggest Hanp1-1Mep: He quits smoking. Avoid making mistakes! repyHA"'i; l'IMeeT Aei;cTBl'ITe11bHb1i; "' cTpaAa- Te11bHb1i; 3anorn, HaCTORl.11ee "' npoweAWee epeMeHa. fepyHAllH B CTpaAaTellbHOM 3a11ore (Passive Gerund): Being+ I appreciate being npi.14acrne II invited to this event repyHAMH e npoweAweM epeMeH11 (Past Gerund): Having + npw-iacTI1e II I appreciate havrng had the opportunity to eet her. fepyHAllH B CTpaAaTellbHOM 3a11ore npoweAwero epeMeH11 (Past-Passive Gerund): Having been + I appreciate having been np1-14acrne II told the news. Cnpsut<eH1t1e rnarona to be To be BblCTynaeT KaK: a) ecnoMorarn11bHb1i; rnaron npi.1 o6pa3oeaHi.1i.1 cpopM Continuous "' Passive 6) rnaron-CBR3Ka B COCTaBHOM l'IMeHHOM CKa- 3yeMOM: He is a teacher HacTOSIUee npoweAwee liYAYUee epeMsi epeMsi epeMsi I am I was I will (shallj be You are You were You will be He, she, it is He, she, it was He, she, it will be We are We were We will (shallj be They are They were They will be BpeMeHa rnarona npocToe HaCTOSIUee (Simple Present, Present Indefinite) npocrne HaCTORl.11ee epeMR o6o3Ha4aeT npi.1- Bbl4Hoe Aei;cTBl'le: TO, 4TO YenoeeK AenaeT Ka:>KAbli; AeHb (HeAento, M8CR4, roA "' T.n.). Children go to school every day. B TpeTbeM 11i.14e eAl'IHCTBeHHoro 4i.1Cna rnaron e Present Indefinite npl'IHl'IMaeT OKOH4aHi.1e -s. Bo ecex OCTaJlbHblX 1li.14ax "' 4i.1Cflax COBnaAa- eT c HeonpeAeJleHHOi; cpopMOi;. I eat, study You eat, study He, she, it eats, studies We eat, study They eat, study BH11MaH11e! One person eats. Two persons eat. One dog barks. Many dogs bark. HacTOSIUee npOAOll>KeHHoe (Present Continuous, Present Progressive) 06pa3yeTCR c noMOl.11bto rnarona to be e Jli.14- Hoi; cpopMe HaCTORl.ljero epeMeHi.1 + np11'iac- T11e I CMb1c11oeoro r11aro11a . 03Ha4aeT Aei;CTBl'le, npOl'ICXOARl.ljee B HaCTO- Rlljl'li; MOMeHT, T.e. B MOMeHT roeopeHl'IR. What are you doing now? I am eating now, at present You are eating He, she. it 1s eatJng Weareeatmg T. ey are ea ng Btt11MaH11e! B npoAon:>KeHHoi; cpopMe He ynoTpe611RtoTCR rnaro11b1: Be Believe Belong Exist Forget Hate Have (B 3Ha4eHl'li.1 «l'IMeTb») Hear Love Need Own Possess Prefer Remember See Think Know Like (e 3Ha4eHi.1i.1 «nonaraTb" ) Understand Want npocTOe npoweAwee (Simple Past, Past Indefinite) 06pa3yeTCR c nOMOl.11blO cycpcpi.1KCa -ed. 03Ha4aeT 3aKOH4eHHoe l'lni.1 npi.1Bbl4Hoe Aei;- CTBl'le B npOWJlOM. YacTO l'IMeeT npi.1 ce6e o6- CTOSIT8JlbCTBa epeMeHl'I: yesterday, last week (month), a year ago etc. What did you do yesterday? I cooked, studied You cooked, studied He, she, it cooked, studied yesterday, last week etc. We cooked, studied They cooked, studied npoweAwee npOAOll>KeHHOe (Past Continuous, Past Progressive) 06pa3yeTCR c noMOl.ljbto rnarona to be e npo- WSAWeM epeMeHl'I + np11'1aCTlle I CMblCllO- eoro rnaro11a. 03Ha4aeT Aei;cTBl'le, Alll'leweecR e onpeAe- 11eHHb1i; MOMeHT B npOWJlOM i.1111'1 OAHOBpe- MeHHO c APYrnM Aei;crnl'!eM e npownoM. What were you doing yesterday at 5 o'clock? What was she doing when you knocked the door? I was reading You were reading yesterday at 5 o 'clock; when someone knocked the door. He, she, it was reading We were reading They were reading npocTOe 6YAYUee (Simple Future, Future Indefinite) 06pa3yeTCR c noMOl.ljbto ecnoMoraTeJlbHOro rnarona will (AllR nepeoro 11i.14a B03MO:>KeH rnaron shall) + llH<l>llHllTllB CMblCllOBOro rnaro11a. 03Ha4aeT 3an11aHi.1poeaHHoe Aei;cTBl'le e 6y- AYLl18M (rnni.14Hb1e 06cTORT8JlbCTea epeMeHi.1: tomorrow, next week, next month etc.) What will you do tomorrow? I will (shallj work You will work He, she, it will work tomorrow; in the evening We will (shall) work in the evening. They will work
6yAy~ee npOAOmKeHHoe (Future Continuous, Future Progressive) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona will (AJll'I nepBoro n1114a B03MO>KeH rnaron shall) + be + «MHroeaJI» ci>opMa CMbl- cnoeoro rnarona. 03Ha4aeT AnlllTenbHoe AeHCTBllle, KOTopoe 6yAeT npOlllCXOAlllTb B 6YAYlJ.1eM n11160 Haxo- AlllTbCS'I Bnpo4ecce BonpeAeneHHblH MOMeHT B 6YAYlJ.1eM. What wilt you be doing at 5 o'clock tomor- row'? I will (shallj be working You wilt be working at 5 o'clock tomorrow. He, she, it will be working We wilt (shalt) be working HacTOR~ coeepweHHoe (Present Perfect) 06pa3yeTCS'I c noMOlJ.1blO BcnoMoraTenbHoro rnarona have B n1114HOH cj:JopMe HacTOS'llJ.1ero BpeMeHlll + Participle II CMb1cnoeoro rnaro- na. 03Ha4aeT: a) AeHCTBllle, Ha4aBweecs:1 BnpownoM 111 He 3aBepweHHoe K MOMeHTY roBopeH111s:1 (Durative Perfect): I have worked since 5 o'clock (and I am still working now). 6) coBepweHHoe B npownoM AeHCTBllle, pe3ynbTaT KOTOporo CKa3blBaeTCS'I B HaCTOS'l- lJ.1eM (Resultative Perfect): I have packed my things (so they are in the suitcase now). I have worked You have worked He, she, it, has worked We have worked They have worked 8HMM8HMe! noKa3aTens:1M111 Heo6XOAlllMOCTlll yn0Tpe6ne- H111s:1 Present Perfect cny>KaT 06cTos:1TenbCTBa BpeMeH111: since (some moment), for (some time), ever, never, already, yet. I have lived here since my childhood. Mary has worked for three hours. Have you ever traveled abroacf? I have never traveled abroad. They have already called me. They haven't called me yet. HacTOR~ee coeepweHHoe npoAon>KeHHoe (Present Perfect Continuous) 06pa3yeTCS'I c noMOlJ.1blO BCnOMOraTenbHOro rnarona have B n1114HOH cj:JopMe HaCTOS'llJ.1ero BpeMeH111 + been + Participle I CMb1cnoeoro rnarona. 03Ha4aeT To >Ke, 4TO 111 Present Perfect Durative, HO nOA4epK111BaeT An111TenbHOCTb AelicTB111s:1: I have been living here since my childhood I have been working You have been working He, she, it has been working We have been working They have been working npoweAwee coeepweHHoe (Past Perfect) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona have B npoweAweM BpeMeH111 (had BO Bcex n1114ax 111 4111cnax) + Participle II CMblCno- eoro rnarona. 03HS4aeT AeHCTBllle B npownoM, npeAwecT- BOBaBwee APYrDMY AeHCTBllllO B npownoM: He had traveled abroad before he entered the uni- versity. I had talked You had talked He. she. it had talked We had talced They had tall<ed npoweAwee coeepweHHoe npoAon>KeHHOe (Past Perfect Continuous) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHoro rnarona have B npoweAWeM BpeMeH111 (had BO Bcex n1114ax 111 4111cnax) + been + Participle II CMb1cnoeoro rnarona 03Ha4aeT TO >Ke, 4TO Past Perfect, HO nOA4ep- KlllBaeT An111TenbHOCTb AelicTB111s:1: He had been traveling abroad before he entered the univer- sity. I had been talking You had been talking He, she, it had been talking We had been talking They had been talking 6yAy~ee coeepweHHoe (Future Perfect) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona will (Ans:1 nepBoro n1114a B03MO>KeH rnaron shall) + have + Participle II CMb1cno- eoro rnarona. 03H848eT AeHCTBllle B 6YAYlJ.1eM, KOTOpoe: a) 6yAeT 3aBepweHo K onpeAeneHHOMY MOMeHTy: He will have finished working by 5 o'clock b) npeAWeCTByeT APYfOMY AeHCTBllllO B 6YAYlJ.1eM: He will have finished working by the time I return. 6YAY~ coeepweHHOB npOAOn>KeHHoe 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTe!lbHOro rnarona will (Ans:! nepBoro n1114a B03MO>KeH rnaron shall) + have + been + Participle II CMblcnoeoro rnarona. 03Ha4aeT TO >Ke, 4TO 111 Future Perfect, HO noA- 4epK111BaeT AnlllTenbHOCTb AeHCTB111s:1: He will have been working by 5 o'clock He will have been working by the time I return. 8HMM8HMe! Hiii OAHO 1113 6YAYlJ.1lllX BpeMeH He ynoTpe6ns:1- eTCS'I BnplllAaT04HblX npeAnO>KeHlllS'I BpeMeHlll Ill ycnOBllll'I, nplllCOeAlllHS'leMblX COI03aMlll Ill COI03- Hb1Mlll cnoBaM111 when, until, by the time, before, if, unless 11 /W I will speak to him when he comes. We shall go to the country if the weather is good. CTpaAaTe11bHb1lit 3a11or (Passive Voice) CTpaAaTenbHblH 3anor 06pa3ye'rcs:1 c noMo- lJ.1blO rnarona to be B HY>KHOH cj:JopMe + Participle II CMb1cnoeoro rnarona Active Voice Simple Present Mary helps John. Passive Voice John is helped by Mary. Present Progressive Mary is helping John is being helped by John. Mary Present Perfect Mary has helped John. Simple Past Mary helped John. Past Progressive Mary was helping John Present Perfect Mary nas heloea John has been helped by Mary. John was helped by Mary. John was being helped by Mary. .na.s been eloed o Mary. Past Perfect Mary had helped John. John had been helped by Mary. Simple Future Mary will help John. John will be helped by Mary. Future Perfect Mary will have helped John. John wilt have been helped by Mary. Ha1116011ee ynoTpe6111TenbHb1e Henpae111nbHb1e rnaronb1 arise arose arisen be was, were been become became become begin began begun bite bit bitten blow blew blown break broke broken bring brought brought buy bought bought catch caught caught come came come cost cost cost cut cut cut deal dealt dealt do did done draw drew drawn eat ate eaten fall felt fallen feed fed fed find found found fly flew flown forget forgot forgotten get got got give gave given go went gone have had had hear heard heard hide hid hidden hold held held keep kept kept know knew known lay laid laid lead led led lend tent lent let let let lie lay lain make made made meet met met pay paid paid read read read ring rang rung run run run see saw seen sell sold sold send sent sent shake shook shaken show showed shown/showed sing sang sung steep slept slept speak spoke spoken stand stood stood swim swam swum take took taken teach taught taught tear tore torn tell told told think thought thought understand understood understood wake woke/waked woken/waked l1Hc/JOpM8LjHOHHO-Cnpaeo~HaR ~ ra6nH4a "'C 000 •llHc/JOnnacr•. 2004 N 0 r. 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HH4'0nAACT TM www.infoplast ru Cnoeapb noec&AHeeHoro o6114eHMH O,qe>1<,qa Clothes BaM 3TO 1<1AeT! It looks good on you! KaKOH y sac paaMep? What's your size? 6enbe underwear 60COHOlKKl-1 sandals 6ornHK1<1 boots 6t0cnanbTep bra rancryK tie AeWeSblH cheap Alt<l-1HCbl jeans AOporoH expensive 30HT umbrella KOlKa leather KOnroTKl-1 pantyhose KOCTIOM suit KoweneK wallet KPYlKBSO lace KynanbHl-1K bathing suit KYPTKa jacket HOCKl-1 socks HOYHaR py6awKa nightgown nanbTO coat nepYaTKl-1 gloves n1-1lt<aMa pajamas nnaTbe dress nnaLJ.1-AOlKAeS1<1K raincoat nORC belt paaMep size py6awKa shirt pyKaS sleeve CS1<1Tep sweater cyMKa bag Tycpn1-1 shoes ¢YT60nKa T-shirt YynKl-1 stockings wanKa cap wapcj:J scarf wenK silk wepcTb wool wnRna hat wopTbl shorts t06Ka skirt ~eern Colours 6elt<eSblH beige 6enb1H white lKenTblH yellow aeneHblH green KOpi.1YH9SblH brown KpaCHblH red opaHlKeSblH orange p030SblH pink cseTnblH light cepblH grey Ci-1Hl-1H blue TeMHblH dark cj:J1-1oneTOSblH purple yepHblH black AeHbrH. 6aHK. noKynKH Money. Bank. To buy CKonbKO R saM AOnlKeH? CKonbKO 3TO CTOl-1T? 5'I 6b1 xoTen... no>Kany~cTa 3To AOporo! nOAasaTb >Kano6y 06Hani.141<1Tb YeK 3aKa3aTb onnaTi.1Tb CYeT 6anaHc 6aHKOSCKl-1H CYeT AaTa nnaTe>Ka AeHbrlol AOCTasKa aa se~ b noA 11Cbl0 How much do I owe you? How much is it? I would like... please It's expensive! to complain to cash a check to order to pay the bill balance bank account matunty date money de ery KOMaHAl-1POSKa KpeA1<1TKa Kypc (santOTbl) MenOYb H8ni.1YHble Hanor o6naraTb HanoroM o6MeHHblH nyHKT onnaTa OTABn npOAalK nepeSOA1<1Tb AeHbrn n1<1CbMeHHO noKynaTenb npOAaSaTb npOAaSel.I npOLeHT pacnpoAa>Ka business trip credit card rate small cash cash tax to tax exchange bureau payment sales department to transfer money in writing customer sell salesclerk interest sale pacXOAbl expenses peKnaMaL11<1R complaint c6epelt<eH1<1R savings CYeT (aa noKynKy, ycnyry) bill TaMO>KHR customs ToprosnR TpaTbl yH1-1sepMar ycnOBl-1R AOCTaBKl-1 ycnos1<1R onnaTbl LieHa l.eHHOCTb 3KOHOMl-1Tb (AeHbri-1) trade spendings department store terms of delivery terms of payment price value save money 3,qopoebe Health rAB y sac 6on1-1T? 5'I ce6R nnoxo YyscTsyt0. 5'I YYSCTBYIO ce6R npeKpacHo! Bbl sb1rnRA1<1Te 6onbHblM. 0TAOXHl-1Te! aHrn61-1ornK aHT1-1cenT1-1K aHrnHa anTeKa 6one3Hb 6onb B ropne 6onb 6pOHXl-1T spay rnnc rpaAYCHl-1K rp1-1nn A1<1arH03 ay6HaR 6onb 1<1HcpeKL1<1R Kann1-1 Kawenb KpOSb neKapCTSO Ma3b Mi.1KCTypa (OT KawnR) OlKOr onyxw1-1H naL11<1eHT nOHOC npocryAa pellem COnHeYHblH O>KOr cpeACTBO TeMnepaTypa (SblCOKaR) TOWHOTa TpaSRHO~ YaH yKon Where does it hurt? I feel sick I feel great! You look sick Rest! antibiotic antiseptic tonsillitis pharmacy illness; disease; sickness sorethroat pain bronchitis doctor cast thermometer flu diagnosis toothache infection drops cough blood medicine ointment cough syrup burn swollen patient indigestion cold recipe sunburn remedy fever nausea herbal tea injection; shot Yiie6a.Pa6oTa Studies. Workplace npOXOA1<1Tb Kypc (no...) (in...) 61-16n1<10TSKa 6i.13H9C-06yYBHl-19 6yxramep 6yxranrnpcK1<1H yYeT SBYepHee (OTAeneH1<1e, o6yYeH1<1e) ryMaH1<1TapHblB HayKl-1 AHesHoe (OTAeneH1<1e, 06yYeH1<1e) AOKn8A BCTeCTSeHHble HayKl-1 3aHRTl-1R 3ay1-1cneH1<1e to take a course library business studies accountant accounting part-time arts; humanities; liberal arts full-time report natural sciences studies enrolment 1<1306pa31<1TenbHOe 1<1CKYCCTBO fine arts 1<1HocTpaHHb1e R3b1K1<1 foreign languages 1<1Hcj:JopMarnKa computer sciences KaMnyc campus Kapbepa career KH1<1ra book KHl-1)f(Hb1H Mara31<1H Konnera KonneAlK Kypc MBCTO pa60Tbl 06paaosaH1-1e Ol.eHKa nonHaR 3aHRTOCTb npaso npenoAaSaTenb pa6orn pacn1-1caH1-1e peKnaMa cnosapb cneL11-1an1-1aaL11<1R cTeneHb 6aKanaspa CTeneHb cj:Ja6p1-1Ka YaCTl-14HaR 3aHRTOCTb WKOna 3K3aMeH 3HL11<1KnoneA1<1R t0P1<1A1<1YecK1<1H cj:JaKynbTeT bookstore colleague college course job education grade full-time work law professor work schedule advertising dictionary major bachelor (BA. , BSc) degree degree factory part-time work school exam encyclopedia law school E,qa. PecTOpaH Food. Restaurant 5'16bl XOTen... 5'I 6bl XOTen 3aKa3aTb... CYeT, nolt<anyHcTa! 06cny>K1-1saH1<1e sKnt0YeHo? 3a CTOnOM s1-1nKa ropY1<1L1a )KapeHaR KapTOWKa 3aSTpaK aaKyeKa Maeno HO)K nepel.I np1-1eM n1<1LJ.11<1 pacT1<1TenbHoe Maeno cancj:JeTKa COnb cneL.11-11<1 CTaKaH Cblp yKcyc yn1<1TKa xne6 I would like... I would like to order. .. The check, please! The service is included? At table fork mustard French fries breakfast appetizer butter knife pepper meal oil napkin salt spices glass cheese vinegar snail bread ftp cup chocolate egg
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I cnoco6: 1) nono>K11M x= 1,23232323... 2) nepeABl1HeM 3anRTYIO Ha DAMH nepM01r IOOx = 123,2323... 3) 113 JOOx BblYTeM x: IOOx-x= 123,23... - 1,23..., 99 -12J _ 122T.e. x- -· 3Ha'll1T x-99 4) l (1')_ 12:! -1 :!311TaK. • -~ - 99 - 99 II cnoco6: 1,.: _ = 1..: - 0. _.)= li --:=1:-=-- - OTHOWeH11e Afll1Hbl n1a6oii OKPY>K- HOCTl1 K ee Al1aMeTpy (.n:- OT rpe'le- CKOro nepwf!ep11R - OKPY>KHOCTb). Llt=- D
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OCHOBHOe CBOiiCTBO ,qpo611: ec1111 '111CJ111Tellb 11 3HaMeHa- Tellb YMHOJKl1Tb 111111 pa3Ae1111Tb Ha OAHO 11 TO JKe '111CJ10, TO no11yY11rc11 pasHaR eii AP06b. 1 1·3 3 3 3:3 I 6= 6-3=18 ' 18 = 18 :3 =6 npMBeCTK AP06K KHaKMeHbWeMy 06lJ.leMy 3HaMeHaremo: 1) Hai1r11 HOK (Ha11MeHbwee o6ll.lee KpaTHoe) 3HaMeHare- 11eii AP06eii, 2) Haiir11 AOnOJlHl1TellbHble MHOJK11Te1111 (pa3- Ae1111Tb HOK Ha KaJKAblii 3HaMeHare11b), 3) YMHOJKl1Tb Y11c- 1111renb 11 3HaMeHaTellb Ha COOTBeTCTBYIOlJ.ll1ii AOnOl1Hl1- TellbHbli1 MHOJKl1Tellb. Hanp11Mep, np11seAeM AP0611 t,t 11 tKo6ll.leMy 3Ha- MeHare1110. ):1111 aTOro HaiiAeM HOK(3, 5, 7) = 3·5·7 =105. Aono11H11re11bHb1e MHOJK11- re1111 y t-3TO 5 11 7' y t-3TO 3 11 7' y t-3TO 3 11 5. 3an11weM 11Xcsepxy, OTA81111B CK06Koii. YMHOJKl1M 11 '111C- 1111T8Jlb 11 3HaMeHaTellb Ha 3Tl1 AOnOl1Hl1T8JlbHble MHOJKl1- Te1111: 1°' 1· 5·7 35 -3-= 3.5.7 = 105 · .r.:::_ = 2·3·7 = 42 5 5.3.7 105 ' 3' 35 3.3 .5 45 -7- = 7.3. 5 105 . CpaBHMTb AP06M: 1) np11secr11 11x K06lJ.leMy 3HaMeHare1110, 2) cpaBHl1Tb Y11c1111re1111 no11y'!eHHblX APD6ei1, 3) cpaBHl1Tb no11y'!eH- Hble AP0611, 11 re JKe 3HaK11y11cXOAHb1X AP06ei1. CpasH11M AP0611 !,t11 t.K o6ll.leMy 3HaMeHare1110 I 35 2 42 3 45 npl1senl1: 3=105 · 5 =105 11 1= 105 · nponop41111 - 3TO paseHCTBO ABYXOTHOWeH11ii. np11Mep· 2 • 5 =12 111111 2 5·5=3 5·7. 5 7 ' . , . Hepa18HCTIO KIWI Ke 113 np11Moro yrna nposeAeHbl KrnnoreHy3e BblCOTa h 11 MeA11aHa. nycTb Bb1cora Ae1111r rnnoreHy3y Ha orpe3Kl1 a 11 b, TOrAa h =.,Joi (113 re0Merp1111). no11os11Ha rnnore- HY3bl - 3TO a;b , a 113 re0Merp1111 3HaeM, '!TO MeA11aHa, nposeAeHHaR KrnnoreHy3e, pasHa no11os11He rnnoreHy- 3bl: m=a;b . TaK11M o6pa30M, HepaseHcTBo Kow11 03Ha- Yaer, '!TO AJ111Ha BblCOTbl, npOB8A8HHOi1 KrnnoreHy3e, ,Apo61 CpasH11M Y11c1111re1111 no11yYeHHblX AP06eii: 35 <42 <45, 3Ha'll1T 11 AP0611 pacno11ara10rc11 a TOM JKe nopRAKe: 35 42 45 105 < I 05 < 105 ' C118AOBaTellbHO, MOJKHO cpaBHl1Tb 11C- XOAHble AP06W t< ~ < t. CnoJKeHKe KBbl'IKTaHMe AP06eii. 1) c OA11HaKOBblM 3HaMeHare11eM (nOABOA11M nOA 06lJ.ll1i1 3HaMeHaT8Jlb 11 CKllaAblBaeM 'll1Clll1Te1111) .!.+ ~= 1+ 2 =l 5 5 5 5 2) c pa3HblMl1 3HaMeHare1111M11 (np11secr11 AP0611 K06lJ.le- MY 3HaMeHare1110, n0Asecr11 noA OAl1H 3HaMeHaTellb, npo- secr11 sb1Y11c11eH1111 c Y11c1111re1111M11): l[' 1<3 5 3 5+3 8 3 + 5=15 + 15 = 15 = 15-. l(J 5<• 3 5 8 4 6 + 18 = !8 +!8 = !8 = 9· YMHOlKeHKe KAeneHKe AP06eii. 'iT06bl nepeMHOJKl1Tb ABe AP0611, HaAO nepeMHOJKl1Tb OT- AellbHO 11x Y11c1111re1111 (3TO 6yAeT Y11c1111re11b) 11 11x 3HaMe- Hare1111 (3TO - 3HaMeHare11b no11yYeHHoii AP0611): 2 4 2-4 8 3·5 = 3-5= 15. 'iT06bl pa3Ae1111Tb OAHY AP06b Ha APYrYID, HaAO nepsylO AP06b YMHO)f(l1Tb Ha «nepeaepHyTy/O» BTOpylD: ~ :~ = ~.i = ~:!= ;~ . 'iT06bl npeACTaBl1Tb 06blKHOBeHHYIO ,qpo6b B811,qe ,qecR- Tl1~HOii, HaAO pa3Ae1111Tb '111CJ111Tellb Ha 3HaMeHaTellb «BCTOJ1611K». np11Mep: l/ 4=0,25, 1/ 3=0,(3) - 6eCKO- He'!Ha!I nep110Al1'!eCKa11 AP06b. 2. .QecRTM'tHble AP06M OKpyrneHMe AO AaHHOro pa3p!!Aa: ec1111 ClleAYIOlJ.la!I l.111QJ- pa 0, I, 2, 3 111111 4, TO 11x npocTO 3aMeHRIOT Hy1111M11, a ec1111 c11eAY10lJ.l11e 411cjlpb1 5, 6, 7, 8, 9, TO noc11eAH1010 OCTaBWYIOCA 411cjlpy yseJ111'111BalOT Ha I, a OCTallbHble 3a- MeH!llOT HYl1AMl1. np11Mep: OKpyr1111M AO COTblX15,3467. 3AeCb 'leTblpe CO- TblX, 3a Hei1-6, 3Ha'!l1T, YersepKy 3aMeH11M Ha 5 (4+ 1), a OCTallbHble 3aMeHl1M HYl1AMl1: 15,3467= 15,3500= 15,35. Dponopq11 MeHbWe 111111 pasHa AJ111He M8A11aHbl, npoBeAeHHOii Krn- noreHy3e: hsm. a b OKpyrn11M AO TblCA'!HblX2,384256. TpeTbR noc11e 3anA- TOii - 4, 3a Heii 2. C11eAosare11bHO, 4 He MeHReM, a see, '!TO 3a Hei1 3aMeHAeM Hy11AM11: 2,384356-2,384000=2,384. CnolKeHKe (Bbl'll1TaH11e) BblnOllHAIOT no pa3PRAaM: AP0611 3an11cb1Ba10TAPYr noA APYrDMTaK, '!T06b1 3anATaA crporo nOA 3anATOii HaXOA1111aCb, 11 BblnOJlHAIOT CJlOJKeH11e (Bbl- 'll1TaH11e) Ha'!11HaA c caMoro npasoro pa3pRAa. CllOJKl1M 3,4682 11 48,63: + 3,4682 48,63 52,0982 v13 67,2 Bbl'!TeM 5,375: _ 67,200 5,375 61 ,825 YMHOJKeHMe BblnOJlHAeTC!I He o6palJ.laA BHl1MaHl1e Ha 3a- nRTble, Bno11yYeHHOM pe3y11bTaTe cnpasa OTC'll1TblBalOT CTOllbKO 3HaKOB AD 3an11TOii, CKOJlbKO 11XCTOl1T noc11e 3a- nRTOii B06011x MHOJKl1Tell!IXBMecre. np11Mep: 3,02 · 1,4 - noc11e 3anATblXscero rp11 3HaKa, 3Ha'!l1T, a no11yYeHHOM pe3y11brare OTAe11AeM 3an11TOii rp11 3HaKa cnpasa: 3,02 x 1,4 1208 + 302 4,228 ,Qe11eHMe. B06e11x AP06Ax nepeHecr11 3amny10 Ha CTOllb- KOl.111QJP snpaso, CKOllbKO 11XBAe1111re11e (TO, Ha '!TO Ae- 1111M) 12,096:2,24 = 1209,6:224; a 3areM Ae1111M Ha 4e- 11oe '111Cl10 B«CTOl1611K»: _1209,61224 illQ__ 5,4 896 896 0 YMHOJKeHMe Ha IO" - nepeHecrn 3an11ry10 Ha n 411cjlp snpaso. np11Mep: 5,238 ·100 = 5,228 ·IO' = 523.8 Pa3AenKTb Ha I0 a creneH11 n - nepeHecr11 3anATYID Ha n 411cjlp s11eso. np11Mep: 2,7: 1000= 2,1:10' =0,0021 A npRMO nponopl.(110HanbHa B c Ko3cjJcjJ111.(11eHTOM nponopl.(l10HanbHO- cr11 k = j .Yse1111'!11s A arp11 pa3a, B yse1111'!11TcR TOJKe arp11 pa3a: 3AeCb 2,5 11 7 - KpaiiH11e '!lleHbl nponop41111, a 5 11 3,5 - cpe,qH11e YlleHbl nponop41111. np0113B8A8Hl1e KpaiiHl1X'!JleHOB = np0113B8A8Hl1IO BHYTP8HHl1X '1118HOB: 2,5·7= 5·3,5 3-A =k·3B, a K03QJQJ11l.111eHT k np11 3TOM He MeHAeTCA k = ~~ . Ase ee1111'!l1Hbl Ha3b1sa10rc11 o6paTHD nponop11MoHanbHblMM, ec1111 np11 yse- 1111'feH1111 OAHOii 113 Hl1XBHeCKOllbKOpa3, BTOpa.R YM8HbWaercR BO CTOJlbKO JKe pa3. A o6paTHO nponopl.(110HanbHa B c K03c/JcjJ111.(11eHTOM nponopl.(110- HanbHDCTH k: A= k i. 'iT06bl HaiiTM HeK3BeCTHblii 'IJleH nponOPllMM, HaAO npOl13B8A8H11e 113BeCT- HblX'!JleHOB pa3Ae1111Tb Ha napHblii '1118H KH8113BeCTHOMy: 0, 3 - 2, 5 .. 2 - = 0 3. - = 0,3. 5 = Q = 0 6 x - 5 ' _, .) . ). x 2.5 2.5 . Ase se1111'!11Hbl Ha3b1sa10rc11 np11Mo nponop11MoHanbHb1 'leHl111 0,11HOM 113 l1X 8 ec Ollb 0 pa3 BTOpa.R yae- HBaeTCll BO .e Pa3 ..f=kB. se,1 ~ B 4 B PM p<Ua, B e b HTCA TO e 8 TPH p33a· 3A = k -% ' 1k=.f B Bell ~ "' ""N "'.., ~ .., 0 ,.._ 0 ..,
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OpraHl13Mbl : 0cHOBHbl8 nonm1<8Hl15l KJ18T04HOH Teop111-1 6b1Jll1 cc:jJopMy.n111posaHbl M. WneHABHOM Ill T. W8aH- 0 npoKap1-1oni14ecK1-1e (6aKTep11111, ClllHe-38Jl8Hb18) - KJ18TKl1 He HOM: see opraHU3Mbl (paCTl1T8nbHb/8 11 )KJABOTHb!B) COCTORT JA3 Kfl8TOK. 1<1MBIOT o¢opMI18HHOro HAPS l<1 MHOrl1X opraHOlllA08; CoepeMeHttaR KneT01..1Has:i Teopiui: o 3yKap1110T1111..1ecK111e {rp116b1, pacTeH11.fl, )l(lll80THb1e, 48Il08eK). 1. K nBTKB ~ BA11H1114a cTpoeH1111 111 pa3e111T1111 0cex opraH1113MOB. 2. KneTKl1 opraHl13M08 pa3HblX 4apCT8 )1(1180lii np11pOAbl CXOAHbl no CTpOBHllllO, Xl1Ml148CKOMY Cyl.J..BCT8Y8T H8KJ18TOYH851 c:jJopMa )l(l-13Hl1 - e111pycb1, KOTOpb18 COCTa8y, o6MeHy 8 8 1.J..8CT8, OCH08HblM npOfl8Jl8H1flM )1(1113H8A8flT8JlbHOCTl1. cnoco6Hb! >Kl1Tb 11 pa3MH0)1(8TbC5l TOJlbKO 8 KJ18TK8X APYrl1X opraHl/13- 3. Ho8bl8 KJ18TKlll o6p83YIOTCfl 8 pe3y.nbTBTe A8I18Hl15l MBT8plllHCKOiii KJ18TKl1. 4. B MHOroKnBT04HOM opraH1113MB KJ18TK11 o6pa3yK)T TKBHlll. 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EcJIH ff (x)dx =F +c , TO crrpaBe,!UIHBa <l><>PMYrra HLIOTOHa-Jleii6mnm: b ff(x)dx = F(b)- F(a) 0cHOBHble CBOHCTBa: b a 1) ff(x)dx=-f f(x)dx b b c b 2) ff(x)dx= ff(x)dx+ ff(x)dx a c b 3) fU(x)+ g(x)-h(x)]dx= a b b b = ff(x)dx+ fg(x)dx- fh(x)dx a b b 4) fcf(x)dx =cf f (x)dx a a 5) ff (x)dx = 0 6) reoMcrpH'!ecK.Hii CMMcrr orrpe,11erreHHoro mrrerparra: ~(x) yb ff(x)dx=S s a b x 7) TeopeMa o6 ou:eHKe H11Terparra: b m(b-a) ~ ff(x)dx ~ M(b-a) a f,11e m - HaHMeHDIIIee 3Ha'feHHe f(x) Ha [a,b]; M - HaH6oJibIIIee 3Ha'feHHe f(x) Ha [a,b]. b 1) ff (x)dx = F(x)I: 2) IIpaBHJIO IIO,!ICTaHOBKH: X =<p(t) b ;-1(b) ff(x)dx= ff[<p(t)] ·<p'(t)dt ;-i(a) 3) mrrerpHpOBaHHe no 'faCTJ1M: b b b ff(x)dx = fudv = uvl:-fvdu a a fipHMep: I I I fxexdx =fxdex =xexl~ - fexdx = 0 0 0 =e-(e - 1) =1 4) rrpH6JIIDKeHHoe Bbl'fHCJieHHe HllTerparros: fipHMep: Yz Bbl'fHCJIHTb I= fe-x'dx c TO'fHOCTblO ,!10 0,0001 0 x2 x4 x6 xs e-x' = 1- 1!+ 2! -3!+ 4!- ... , 3Ha'fBT, , x2 x4 x6 x fe-x dx= x(l -1!·3 + 2~5 - 3~7 + 4~9 - ...). OTK}',!13 Yz 2 1 1 1 I= fe-x dx=l(l- 22 ·3·1!+ 24 ·5·2!- o 1 1 - + - ...)"" 0,4613 26 . 7 .3! 28 . 9 .4! Pa3nO>KeH"1e OCHOBHblX <l>YHK4"1M B P~Abl m(m-1) 2 (l ± xr = l±mx+ 2, x + ...+ nm(m-1)...(m -n+l) "+ lj<l· +(-1) x ..., ..1 ' n! 3 5 2n+l . x x l)" x + .sm x=x--+-- ...+(- -···· 3! 5! (2n +1)! 2 4 x2n COSX = 1- .::.._+.::__-...+ (-1)"--±...; 2! 4! (2n)! 2 xn x 1 x . x + + .e = +- + -+... - ..., 1! 2! n! x2 x3 ln(l+x) = x-2 +3-...+ + (-lr+'xn ± ..., (-l<x~l). n 5) rrpH6JIIDKemn.1e MeTO,!lbI: ipopM)'rra IIpllMOyrOJlbHHKOB b b-a ff(x)dx"" -n-(Yo + Y1 + ...+ Yn-1) a ipopM)'rra T}JaIIeiulli b b-a f f(x)dx ""--(y0 +2y1+2y2+ ...+ 2n ) a +2Yn-I+Yn <l><>PMYJI3 rrapa6orr (CHMIICOHa) - .!IJIJl 'feTHOro n: b b-a f f(x)dx,,,,--(Yo +4y1 + 2y2 +4y3 + 3n a +...+2Yn-2+4Yn-I+ Yn) ( +br+' f (ax +b)"dx ax + c,(n :t:-1) a(n+ 1) f ax+b dx=~x+ bf-,ag Inlfx+ gl+c fx + g f 1- dx f(ax+b)(fx+ g) fax2 +~x+c = 2 l 1nlfx + g l+c, bf - ag ax +b (bf - ag :t: 0) =-===arctg - --- c. ...., 4ac - b- fax2 :;,x+c = 1 2ax+b-"1b2-4ac - ===ln +c, -..)b2- 4ac 2ax+b +-..Jb2- 4ac (b2 - 4ac >0) f~(ax+:fx+g) = _2_Inl~a(fx+ g) +~f(ax+b)l +c, -{<if af >O 2 ~arctg -v - af f(ax+b) +c, af <0 a(fx+ g) f~fx+ g dx = _!_~(ax+b)(fx+ g)- ax+b a bf-ag f dx +c 2a ~(ax+ b)(fx +g) ' f"1a2-x2dx= = _!_ (x"1a2- x2+ a2arcsin ~) + c 2 a f"1x2 +a2dx = = ~(x"1x2 +a2+a2lnlx+"1x2+a2i) + c f"1x2-a2dx= = ~(x"1x2 -a2- a2 Inlx+"1x2-a2 i) + c f sin ax xcosax xsinaxdx=- -2 - - +c a a f cos ax xsin ax xcosaxdx=--2 -+ +c a a fInxdx=xlnx-x+c f . x . x rz-2) arcsm - dx = xarcsm-+ '/a- - x- + c a a f x x rz-2)arccos-dx = xarccos--'Ja- - x- +c a a f x x a I 2 2I)arctg-dx = xarctg---In a +x +c a a 2 farcctg ~dx = x a .1 , 21)= xarcctg-+-In a- + x +c a 2 ::- l E
A CQ) Q A+B HJill AuB B A CQ) Q AB HJill AnB B A CQ) Q A-B HJill A B B A CQ) Q A B A H B - co6brrHl!. CaoiicTBa co6hrrHii: l. A+B=B+A 2. (A+B)+C =A+ (B+C) = A+B+C 3. AB=BA 4. (AB)C = A(BC) =ABC 5. A(B+C)=AB+AC P(A)- aepoJITHOCTh crryqaiiHoro co6hITHll A 1. O~P(A)~l 2. BepoJITHOCTh )l;OCToaepHoro co6hrrHll paaHa 1 3. BepoJITHOCTh HeB03MO:lKHoro co6hrrHll paaHa 0 TeopeMLt CJIOllCeuu11 u yMuollCenuH eepoHTHOCTeii. TeopeMa cJIO)KeHHl! aepoJITHOCTeii: P(A+B+ ...+Z) = = P(A)+P(B)+ ...+P(Z), ecJIH co6hITHll He33BHCHMhI. P(A+ B) = P(A)+ P(B)-P(AB), ecJIH co6brrHll 3aBHCHMhI. Cne.LlCTBHe: P(A) = 1- P(A) P(AB..Z) = P(A)P(B)...P(Z) , ecJIH co6hITHll He3aBHCHMhI. P(AB) = P(A)PA(B)+ P(B)P8 (A) (r.le P,._ (B) H P8 (A )-ycnOBHhie aepoJITHOCTH), ec.TH cofihITHJI 33BHClillhl. lfucno pa3MeJ.I.1eHHii H3 n JneMeHTOB no m: A,~ = n(n - l)(n - 2)...(n - m + 1) A;;'= n! (n-m)! lfucno pa3MeJ.I.1eHHii H3 n JJieMeHToB no m CnOBTOpeHHl!MH: A,,m = n! (n-m)! lfucno coqeTaHHii H3 n JJieMeHTOB no m: cm= n(n-l)(n-2)...(n-m+l) n I I m. cm= n. n m!(n-m)! lfucno coqcraHHii H3 n JJieMeHTOB no m CnOBTOpeHHl!MH: c: = c:+m-l Caoiicraa qncna coqeraHHii: c: = c;-m lfucno nepeCTaHOBOK H3 n 3JieMeHTOB: P,, = n! Cl>opMYJia 6HHOMa llilOTOHa: (a +b)" = C~a" + C!a"-1b + c;a"-2b2 + p (A)= P(AB). p (B) = P(AB) B P(B) , A P(A) <l>OPMYJI3 nOJIHOH aepoJITHOCTH: n P(A) = L P(Bk)PB, (A), k=l B1, B2 , ••• , Bn He3aBHCHMhl H o6pa3)'IOT nOJIH)'IO rpyrrny COOhITHH, n T.e. LP(Bk)=l k=l P(Bk)P8 (A) <l>OPMYJia Eaiieca: PA (Bk)= n k 0.5 P(m) 0.4 0.3 0.2 0. 1 p=0.2 LP(Bk)PB, (A) n=5 2 3 p=0.8 4 <l>yHKIUfJI pacrrpe.ZJ;erreHIDI: F(x) =LP(X =x) X;<X P(a s X s b) =F(b)-F(a) n M[X]= LX;P; i=l ~crrepcID1: D[X] =M[(X - M[X])2 ] n D[X] =L(X; -M[X])2 pi i=l D[X] =M[X 2 ]-(M[X])2 Cpe.1U1ee KBa.ZJ;panf'rnoe orKJioHeHHe: ax= -JD[X] b P(a < X <b) =Jf(x)dx, a f (x) - IIJIOTHOCTh aepoHTHOCTH <l>yHKIUfJI pacrrpe.ZJ;eneHIDI: x F(x) = ff(t)dt MareMaTH'ieCKoe OJKII.ZJ;aHHe: -mx =f.xf(x)dx ~crrepcIDI: -Dx = J(x -mx)2 f (x)dx M(X) =np D(X) =npq m5
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l. IlpOH.3BOJJbHbIH TJJeyrOJJblUiK c>b~y > ~ ~C)'M;-..ia yrnoe TJJeyrOJJhHHKa a+~+y= 180° BttewttHH yroJJ 'IpeyroJJ&HHKa b=a+~ TeopeMa KOCllHYCOB b2 = a2 + c2 - 2ac cos ~ TeopeMa CHH)'COB _a_=_b_ =_c_= 2R sin a sin ~ sin y (zoe R - paouyconucaH1wu 0Kpy:J1CHocmu). ~S =2-ah 2 a l . P. S=-acsml"' 2 S = ~p(p - aXp-bAfJ - c), a+b+c zoe n011ynepw.•emp p = 2 l(eHTJl OilHCaHHOH OKpy11rnoc- TH - TOqKa nepece4eHllJI cepe- .llHHllblX nepneH,llHKYJJJlpOB. R= abc 4S l(eBTJl em1caHHOH OKpyll(}lOCTM - TOLfKa nepecetJeHl.UI 6HCCeK1'pHC. 2S r=--- a+b+c HeK0Topb1e csoH.crna Me,[(11a11, 611cceKTp11c 11 BblCOT Meoua11bl nepeceKwomCJt 6 00/IOU mo~Ke u mo~KOU nepece~eliW! OeJU1mc11 6 om11owe11uu 2 : I. c~uma11 om 6epwu11bl. h~C ~a Ilpl!MoyrOJJbHblH 'IpeyrOJlbHl1K c TeopeMa Iillljlaropa. c2 = a2+ b2 S= ab 2 ,lJ,n11tta OKpy)l(HOCTH C = 2nR, IlJJOl..llaJlb Kpyra S = nR. 2 R nR. 2 • CV IlnoIU3Jlb Kpyrosoro ceKTopa no l s = -36_0_0 · nnR • b c--:. f"i:""':. MHHa t1yrH l =--0-. n h=!!__=~acbc; a=vacc; b=vbcc 0 180 c ti (n - 2paoyCHaJ1 .Mepa •feHmpanbHOZO yZ11a) . b a IlnOIU3Jlh Kpyrosoro cerMett 2 Ta sm a=-;;; cosa=c b @ rrR o 1 R2 . o S =--·n ± - sm n a b 36if 2 ctg a= b; tg a=~ R 3HaK «+» Haoo 6pamb, Ko2oa ECJ1u ~ =30°, mo c =2a. Q n° 180° < n° < 360°, a 31/aK «-» llQOO PaJ1ttyC snHCaHHOH oKpy)l(Hocrn: ab a+b-c r r a+b+c 2 c PaJ111yc om1caHHOH OKp)l)KHOCTM R = - 2 I . Dpo113soJJbHhii1 4eTb1pexyronbtt11K ~qeTblpexyroJlbHHK, o nHcaHHblH OKOJIO OKpy ll(}lOCTH {Js h dd r=- = - ' - 2; 2 4a s a +c= b + d a+b+ c+ d 2 S = aha = bhb S = ab sin a ·r d 2 + d 2 - 2(a2 +b2 )I 2- S d1d2sin rp 2 S = d1d2 2 S = ah. = 2ar = a 2 sin a. 4. IlpllMOyrOJJbHl1K S = ab = d 2sin rp 2 5. Tpanel(HJI (h - 6blCOma, di. d2- oua20Ha.w) EF= a+b . S= d1d2 sinrp 2 . 2 a-b S= - - ·h = EF ·h..., 6pamb, K0200 0°< n ° < 180°, ( n° - zpaoyc11aJ1 A1epa i;e11mpanbHOZO yZ11a) HeKOTOp&1e ceoiiCTBa en11catt111>1x yTJJoe: I . Bnuca1111blu y20J1 pa«e11 no!IOBUHe J.feHmpa!lb· HOzo y2J1a, onupG/ouiezoc11 11a my :J/Ce oyzy; (6nllCGllllblU y20J1 pa8e/I nO!I06U/le oyzu, 110 Komopy10 OH onupaemc11). a=~=_!_! 2 2 2. BnucaH1tble Y2llb1, onupa10uiueCJ1. Ha ooHy u my :J1Ce oyzy, pa6/lbl. 3. Bnuca1111ble Y2llbl, onupa10uiueCJ1. 11a oua.Memp, npR.Mbte CooT11ouieHl1ll: Me)l()zy ,[(Jll1HaM11 xopA, OTPe3KOB KacaTeJJbHhIX 11 ceKyIUHX I. ab = cd 2. AB =AC ~ An4. AD-AE = AB-AC £J §)A D A ilnOIUllJlb, PllJIHYCbl BIIHCaHHOH 11 01111caHHOH OKPY)l(HOCTeH (a - cmopo1w, r - paouyc snuca1111ou 0Kpy:J1C11ocmu, R- paouyc onuca1111ou oKpY:JICHOcmu). r R s a a a 2/J lpeyrOJJbHHK 2,./3 J3 -- 4 a a a2KBllJIPaT - Ii2 a/3 a 3a 2 /3wecmyro.nhHHK -- --- 2 2 a a a2 n fl · )T0.1b HHX ..., 180°1 ..., . 180° 1 0° _tg- - ~sm -- 4 tg-~ n n n
HQ nJIOCKOcmu l. PaccTOsim1e Me)!(L()' ToqKaMH A(x1; y 1) 11 B(x2;Y2) _ f( _ )2 ( _ )2AB - v X2 X1 + Y2 Y1 2. Koop,1111HaTbI (x; y) cepe,11HHbI OTpe3Ka c KOHllaMH A(x1;Yi) 11 B(x2; Y2) X1 +X2 y = Y1 +Y2 x=-2- , 2 3. 06ll.lee ypaimett11e npsiMoi1, nepnettn11Ky- 11sipttoH. BeKTOpy n(a;b) ax+ by+ c = 0 4. Ypasttett11e 0Kpy:>ICHocn1 c pa,1111ycoM R 11 c 1..1ettTPOM s rnqKe (xo; Yo) (x-xo)2 +(y-yo)2 = Ri 5. EcJJH A(x1;y1) 11 B(x2;y2), TO Koop,1111ttaTbJ BeKTOpa: - ( ) AB X2 -x1:Y2 - Y1 MO.llYJlb BeKTOpa: iAsi=~~(x-2--x-1)2-+-(Y_2___Y1-)2 6. CJJO)l(ett11e seKTopos a(a1;a2)+b(b1;bi}=c(a1 +b1;a2 +bi} 7. YMHO)l(ett11e seKTopa(~) Ha 'IHCJJoA (a1; a2 ) A= (Aa1; Aa2) 8. CKanS!pttoe npOH3Be,!leHJ1e BeKTOpOB aMb ; ·b = l;l·lbl·cosq;, f,!le (/) - yroJJ Me)l(,!ly BeKTOpaMH QM lJ 9. CKaJJsipttoe npoH3se,11ett11e seKTopos a(al; G2) H b(b1;b2) a·b = a1b1+a2b2 I0. Koc1myc yrna Me)l(,!ly seKrnpaMH a(al; G2) H b(b1; b2) a·b a1b1+a2b2 cos <p =-=-=- =-----,,= ====----;===== lal·lbl ~a12 + a; .~b12 +b; 11. Heo6xo,1111Moe 11 nocTaTO'IHoe ycJJos11e nepneH.llHKYllS!pHOCTH BeKTOpOB ;(a1;aJ 11 b(b1;b2) a·b=0 MilM a1b1 +a2b2 =0 W (R paouyc oc1106m11<11 11wm11opa) 2 s 6oK= 2rrRH; v= rr.R H ; s nonH= 2rr.R(R + H) (R - paouyc OCH06G/IUJI KOuyca. - o6pG3ylOU(aJI KOH)'CG) 1 2 s 60K = TTRZ; v =3TTR H ; SllORH = rr.R(R +1) (R1 u R2 paiJuycw ocH06aH111i KoHyca, I 06pG3y1011JGJ1 KOHyca) S""'" =1t(R1 +RJI - -.r(R1 2 + R~) I~ BnpocmpaHcmBe l. PaccTOSIHHe Me)!{,11y TOqKaMH A(x1; y 1; z1) 11 B(x2; Y2; z2) - ------------- AB= ~(x2 -x1)2 +(Y2 -y1) 2 +(z2 -z1)2 2. Koop,1111ttaThl (x; y; z) cepe,11HllliI OTPe3Ka c KOHUaMH A(x1;y 1;z1) H B(x2; Y2; z2) X1 + X2 y = Y1 + Y2 z = Z1 + Z2 x=-2-, 2 2 3. 06mee ypasttett11e nJJOCKOCTH, nepnettn11- KyJ1S1pHoH BeKTOpy n(a;b; C) ax + by + cz + d = 0 4. YpasHeHHe c¢epb1 c pa,1111ycoM R 11 c 1..1eHTPOM B TO'IKe (xo; Yo; zo) (x-x0)2 +(y-y0 )2 +(z-z0)2 = R2 5. EcJJH A(x1; Y1; z1) H B(x2; Y2; z2), TO KOOp,!IHHaTbl BeKTOpa AB(x2 -x1;y2 -y1;z2 -z1) MO,!lyJlb BeKTopa IABI =~-(x-2---X1_)2_+_(_Y2___Y_1)-2-+-(z-2---z1-)2 6. C11o)!{eHHe seKTopos ;(a1;a2;a3)+ +b(b1;b2;b3)= ~(a1+b1; a2+b2; a3+b3) 7. YMHO)l(eHHe BeKTopa (~1;a2;G3)Ha '111CJJO , (a1; a2; a3) ,= (J.a1;Aa2; Aa3) 8. CKansipttoe npOH3Be,!leHHe BeKTopOB aH b ; .b= 1;1·lbl. cos(/), r,11e cp - yron Me)l(,!ly seKTopaMH a Mb 9. CKMJ1pttoe npo113se,11ett11e seKTOpos ;(a1;a2;a3 ) 11 b(b1;b2;bJ a·b = a1b1+a2b2+a3b3 I0. Koc11ttyc yrna Me)l(,!ly seKTopaMH ;(a1;a2;a3 ) H b(b1;b2;b3 ) a.b a1b1 + a2b2 + a3b3 cos (/) =-=-=- =---;:=:::i::::::===----"-o=="====- lal·lbl ~a12 +a;+a; ·~b12 +bi+bi 11. Heo6xo,1111Moe 11 ,11ocTaTO'llloe ycJJos11e nepneH,!IHKYJJS!pHOCTH BeKTOpOB ;(a1;a2;a3) 11 b(b1;b2;bJ Sc</Jepbl = 4n.R2; Vmapa= ~ 7T. R3 4acrn wapa 1. lllapoeoil cer MeHT (h 6blcoma ceZA1e11ma) 9, V=nh'(R-H s 60K = 2rr.Rh 2. lllapoeoil ceKTop (h - B1>1coma cezwe11ma) ~ s llOlH = nR(2h+~2Rh-h2 } ~ V =3._rr.R2 h 3 3. lllapoBOH C.lOH (h Bblcoma CIOR} I : 1 : : V= - ith + - ;r 'i + r- h: 6 2 - s = _ ;rRh 0603Ha'leHHS!: H Bbtcomo, S00• - ruioz1.1oob 60K0601/ n0Bepx11ocmu, S""''" - tUIOllfOOb noJ111oii no6epx11ocmu, V - o6oi!M. (Soc,,- fl.llOUJGOb 0C/106GHUJI, p - nepUMemp OCH08G/lllJ1) I. 2. 3. HaKJIOHHaJI npli3Ma (I - 6oK060e pe6po, Pce4 - nep1wemp nepne11ouKyJ111p110- 20 ce4e11u11, Sce4 fl.llOllJGOb nepne110UK)1J1Jlp11020 ce4e111<11) S OOK = Pc••l; V = See.I = Soc11H; SnOAH= S6oK + 2 SoCH IlpllMaJI np113Ma Riff Ljj S6oK= Poc11 H; V = Soc11 H; snORH= S6oK + 2SOC/I IlpllMOyronbHhIH napa!lnenemme,[l (a, b, c - ezo U3.Mepe11W1, d - OU02011Q/lb) d 2= a2+b 2+c2; V =abc; Sno.•11 = 2(ab + be + ac) 4. Ky6 (o - pe6po) a@ d = a,./3; V = a3 ; (I - ano</JeMa) 2. IlpaBHilhHall ID!paMH,[la I - nepu.1i1emp oc1106011W1} S =.J:._P·l60K 2 3. IlpOHJBOJihHaJI yceqeHHaJI mtpaMH,[la ~ (S, u S2 - nllOUJao11 oc1106011uii) C1? Sno,,,, =S60K+S,+S2; v= }__ H. (s1+s2+~s1si}3 4. IlpaBHilbHaJI yceqeHHaJI nHpaMH,[la (P1u Pi - nepuMempbt oc1106011u1i) l!!s>S'"' =~(P,+P,) I 11HqlopMilljHOHHO-Cnpaao4HaR ra6n"1jil C OOO '1H<Ponnacr-. 2004 r. Mocl<Sa. KaJJMpCKoe wocce. 21 E-mat ~"' ... iJIOOfast. llJ 0
PaanM'IHb1e BMAbl yrnoa A 0 Aea yrna Ha3b1Ba10TCH cMe)f(HblMl1, ecn11 y H111X OAHa CTOPOHa 06LI.1a5!, a Apyr111e CTOPOHbl 51Bn51- IOTC51 AOnOJlHl1TellbHblMl1 ny'laMl1. LAOB 111 LAOC- CMe)f(Hble yrllbl. • CYMMa CMe)f(HblX yrnoe pasHa 180° A B 0 c D Aea yrna Ha3b1Ba10TCH sepTMK311bHblMM, ecn111 CTOPOHbl OAHOro yrna 51Bfl5llOTC51 AOnOllH11Tellb- HblMl1 11y'laM111 cTopoH APYroro yrna. LAOB 11 LDOC eepT111KallbHbl8, LAOD 111 L.BOC eepT111KallbHble. • eepT11KanbH01e yrnb1pasHbl (LAOB = LDOC; LAOD = LBOC). a A B I 1 /2I b I D C 1 I np51Ma51 AC Ha3b1saeTcH ceKy1qeii no oTHowe- H11110 KnpHMblM AB 11 CD, ec11111 oHa nepeceKaeT o6e npHMb1e. Ecn11 np51Ma51AC51BnReTC51 ceKy- LI.1911 no OTHoweH11110 K np51Mb1MAB, CD 111, Kpo- Me Toro, TO'IK111 B 11 DJ19)f(aT BOAHOJil nonynno- CKOCT111 OT ceKyLI.1el1 AC, TOyrnbl BAC 111 DCA Ha3b1BalOTCR BHYTP8HHMMM OAHOCTOPOHHMMM. a B A D Ecn11 AC- ceKyUaR no OTHOWeH1110 AB 11 CD, a TO'IKl1 B 111 D ne)f(aT s pa3Hb1X no11ynnocKo- cT5IX OT AC, To yr11b1BAC11 DCA Ha3blBalOTC51 BHyTpeHHMMM HaKpecr nelK31qMMM. a " 3 1 b Coo1se1c1seHHbtMM Ha3b1BalOTC51 yrnb1npR- MblX a, b c ceKyLI.1el1. Yrllbl 1 111 3 - COOTBeTCTB8HHble. 06PA30BAHME YacTb 2 ~ noc1poeHHe rpMryp AeneHMe otpe3Ka nononaM . c. A 0 ; c, nocrpoeHMe. 1113 TO'leK A 11 B l.lli1PKY119M on111cb1saeTcsi oKpy)f(- HOCTb pa,o,111ycoM AB. nycTb c11 C, - TO'IK111 nepece'l9Hl151 3Tl1X OKpy)f(HOCTel1. 0Hl1 ne>KaT B pa3HblX nonynnOCKOCTRX OTHOC111T91lbHO np51MOJil AB. COOMOUblO 11111H9JilKl1 C08A111Hl1Tb TO'lK111 C 111 C,. 0Tpe30K CC, nepeceKaeT oTpe3oK AB a TO'!Ke 0. 3Ta TO'lKa - C9P9Al1Ha 0Tpe3Ka AB. npoB8A8HH8 nepneHAHKynRpa KAaHHOH np!IMOH '-lepe3 TOYKY 0 npoeecT11 np51MYIO, nepneHA111KYl151PHYIO ,QaH- HOJil np51MOl1 a. PeweHMe. Bo3MO>t<Hbl ,o,sa cny'la51: 1) TO'lKa 0 119>Kl1T Ha np51MOl1 a; 2) TOYKa 0 He 118>K111T Ha npSlMOJil a. Cny'laif 1 . ..c B 0 a nocTpoeHMe. 0Tfl0)f(l1M OT TOYK111 0 no pa3Hble CTOPOHbl OT Hee Ha np51MOJil a o,o,111Hai<o0b1e oTpe3Kl1 OA, OB. npoeeAeM ,o,ee OKPY>KHOCT111 OA111HaKoeoro pa,o,11yca A.Bc l.l9HTPOM a TO'l- Kax A 11 B cooTBeTCTBeHHO. OH111 nepeceKaioTcsi a TO'lKe C. npoee,o,eM npsiMyl-0 (QC). 0Ha nepneH,0,11KY!151pHa np51MOl1 a. A Cny'laii 2 :· 0 . o, B a nocTpoeHMe. npose,o,eM OKPY)t(HOCTb c l.l0HTPOM 8 TOYKe 0, nepeceKalOUYIO npRMYIO a BABYX TO'IKax A 111 B. npose,o,eM ABe OKPY>KHocT111 c l.l8HTpaM11 e TO'IKax A 11 B 111 paA11ycoM, paBHblM OA. nycTb O, - TOYKa nepece'l8H1115l, OTl111'1Ha5l OT TO'IKl1 0, (0 111 O, ne)l(aT e pa3Hb1X nonynnocKOCT51X). Tor,o,a npsiMaH (00,) nepneH,o,11KynsipHa ,QaHHOl1 npsiMol1 a. noctpoeHMe tpeyronbHHKa no tpeM ctopoHaM nocrp0111Tb TpeyronbH111K c AaHHblMl1 CTOPOHaM111 a, b, c. A 4 b b a c c B c noc1poeHMe. CnoMOUblO n11Hel1K111 npoee,o,eM npo113sonbHY10 npHMYIO 11 OTMeT111M Ha Hel1 npo113sOnbHYIO TOYKY B. PacTso- poM l.l11PKynsi, pasHblM c, on11cb1saeM OKPY>KHOCTb c l.l0HTPOM BTO'IKe B 111 P3A11YCOM c. nycTb c- TO'IKa ee nepece'!9H1115l c npsiMO~. ,[anee on11cb1BaeM OKP~HOCTb c l.l0HTpOM BTO'l- Ke B paA11yca a 111 c l.l8HTPOM BTO'lKe cP3A111YCa b. nycTb A - Td'IKa nepece'leH1115I nocrpoeHHblX OKPY>KHOCTeli. Tpeyronb- Hl1K ABC- 11CKOMblJil. noc1poeHM8 yrna, paBHOfO A3HHOMY 0TllO>Kll1Tb OT AaHHOfO ny'la B,o,aHHYIO nonynnoCKOCTb yron, paBHblJil ,o,aHHOMY yrny. c c, . A · B nocTpoeHMe. npose,o,eM OKp~HOCTb c 4eHTPOM Beepw11He ,o,aHHOfO yrna. nycTb B 11 c-TO'IKl1 nepeceY8H11151 OKPY>KHOCTl1 co cTopoHaM111 yrna. PaA·111ycoM AB npose,o,eM oKp~HoCTb c l.l9HTPOM BTOYKe A,- Ha4anbHOJil TO'IKe ,o,aHHOro J1Y'fa. TO'IKY nepeceYeH1115I 3TOJil OKP~HOCTl1 c ,o,aHHblMny'IOM o603Ha- '1111M B1• On111weM oKp~HOCTb c l.l8HTpoM BB1 11 P3A1'1YCOM BC. TO'lKa nepece<ieH111R C, nocTpOeHHblX OKP~HOCTeli ByKa3aH- Hol1 nonynnoCKOCT111 ne>K111T Ha CTOPOHe 11CKOMoro yrna. 00CTpOeHM8 6HCC8KTpMCbl yrna noeTp0111Tb 611CC8KTp111cy ,[J,3HHOrO yrna. B noc1poeHMe. 1113 eepW1'1Hbl O,o,aHHoro yrna, KaK 1113 4eHrpa, on11weM OKPY>KHOCTb np01113BOllbHOro pa,o,111yca. nycTb B 11 c - TOYK111 nepeceYeH11si ee co cTopoHaM1'1 yrna. nocTpo11M eUe ,o,ee OKPY>KHOCT11 c reM >Ke pa,o,11ycoM c l8HTpaM11 a B 1-1 C. nycTb D- TOYKa 11X nepeceYeHl151. Tor,o,a [AD) - 11CKOMaR 6111cceKTp111ca yrna A. nposeaeHMe np1Moit, napannenbHOM aaHHOH Yepe3 3a,QaHHYIO TOYKY A npoeecT11 npsiMylO, napannenbHYIO AaHHOl1 np51MOJil a. D .rA ... ' a I I I · B c nocTpoeHMe. '-lepe3 33,QaHHYIO TO'IKYA 11 npo113BOllbHYIO TOY- KY B npHMOJil a npose,o,eM npsiMy10 AB. nycTb C - npo113- BOl1bHa51, OTl1111'1Ha51 OTB TO'IKa np5lMOl1 a. nocTp01'1M OTnyya AB B nonynnocKOCTb, He co,o,ep>KaUYIO TOYKY C, yron, pas- Hb11il yrny (ABC). nycTb [AD) - CTdpOHa nocTpOeHHOrO yrna. Tor,o,a np51MaA AD II a. 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Asa- np11MoyronbHb11 tpeyronbilHKa ffOA06Hbt. ecnM: 1) uxK-a:rer1J1.nponapl.f~HMbH_bJ; ~=----------~ 2) KarerHr11n_ore1;1y3a opHo.ro rpeyFotTbf!JtKa njJo- nopl.f"lfOHaJlbHb.l ~aJ.BT.JI J.1 PY.flOT8H¥38J[py.rexi'.o; .3j' lfBa yrna O!JHOro rpeyronbH/l!*a11affffbl 1J8YM.yrnaM 11pyrora~ . ' HH<t>opMal.IHOHHO- cnpaeo'iHaff Ta611HL1a © 0 00 «V1Hcpon11acr", 2006 no;o,nHC8Htj a ne•aTb 28. 12.os. r..pa)I( 40003K3. 3ali'.a3 t-P 3106. "13,qarenb 000 •fl1H¢onnacr», Moci<ea, Kaw'1pcKoe wocce, 21. r..notpa</>MR ooo.s..sa-Crap•, 107023, MocKsa, yn. 311eKTposa1JOp.CK8A, 20 -
3nnMnCOM Ha3blBaeTC!I reOM0TPl1'l0CK00 M0CTO TO'l0K, CYMMa paCCTO!IHl111 OT KOTOPblX AO ABYX 3aAaHHblX TO'l0K F, 11 F;, Ha3b1saeMb1x itioKYC3MM 3nn11nca, ecrb sen11'111- Ha OOCTO!IHHaR. 2 2 YpaaHeHMe 3nnMnca: x2 + y2 = I . (I b 3A0Cb HaYano KOOPAl1Har !IBn!leTc!I 4eHTPOM c11MMerp1111 31111110Ca, a OCl1 KOOPAl1HaT - ero OC!IMl1 Cl1MM0Tpl111. np11 a >b ¢0Kycb1 3111111nca neJKaT Ha oc11 OX, np11 a <b ¢oKyCbl 3111111nca neJKaT Ha oc11 0 Y. a np11 a = b3nn11nc craHos11rc11 oKpYJKHOCTblO (¢0Kycb1 3nn11nca B3TOM CJlyYae COBOaAalOT c 4eHTpOM OKPYJKHOCT11). TaKl1M o6- pa30M, oKpy)l(HOCTb ecrb '18CTHbti1 cny'lai1 3nn11nca. Orpe30K F.Fi = 2c, rAe c = ~la2 -b2 I ,Ha3b1eaerc11 itio- KYCHblM paccro11HMeM. To'iK11 A, B, C 11 DHa3b1Ba10TC!I aepwMHaMM 3nnMnca. Orpe30K AB = 2a Ha3b1eaerc11 6onbwoii OCblO 3nnMnca, a orpe30K CD = 2b - Manoii , ,2 YpaaHeHMe rMnep6onbl MMeeT BMA: 4-~ = I . a b 3TO ypaBH0Hl1e Ha3b1Baerc!I KaHOHl1'i9CKl1M ypaBH0Hl19M r1o1nep6onbl. Caoiicrao. r11nep6ona He "1Meer 061J.111X TO'l0K c OCblO Oy, a OCb Ox nepeceKaer s ABYX TO'IKax A(-a; 0) 11 B(a; 0), KOTOPblB Ha3bl83IOTC!I eepWMH3MM r 11nep60llbl. Orpe30K AB Ha3b1eaeTC!I AeiicTBMTenbHOii ocbio r11nep- 6onb1, ero An11Ha paeHa 2a. 'i11c110 a Ha3b1Baerc!I Aeiicr- BMr enbHOii nonyocblO r11nep6011b1, Yli!CllO b - MHMMOii no- nyocblO. CeoiiCTBO. r1i1nep6ona 11M00T ABB B3al1MHO nepneH,!111KY- Jl!IPHble OCl1 Cl1MM0Tpl111. <1>11rypa, Ka)KAa!I TOYKa KOTOpol:l pasHoy,11a11eHa OT AaHHOlii TOYK11 A 1i1 ,11aHHOlii npsiMolii I HaJb1saeTcS1 napa6011olii. y 2 = 2px 3ro ypaBH0Hl1e H33bl830TC!I KaHOHl1'i0CK"1M ypaeHeHl10M napa6011b1. 06PA30BAHME 3nnMnc c OCblO 3nnMnca. 'il1CJ10 6 =a' E < I Ha3blBaeTC!I 3KC"eH- TpMCMT0TOM 3nnMnca. F,M =a+tx, F,M =a-ex Caoiicrao. CyMMa paccroS1H11i1 or n106ol1 TO'iKl1 3nn11nca AO ero ¢oKyCOB eCTb een11Y11Ha nOCTO!IHHa!I 11 paeHa!I YABOBHHOlii 6011bwel1 no11yoc11. F,M+F,M = a+sx+a- sx =2a Caoiicrao. 311n1,1nc 11Meer ABB s3a11MHO nepneHAl1Ky1111p- Hb1e OCl1 CIAMMeTplAl1. Caoiicrao. 3nn11nc "1Meer 4eHrp c11MMerp1111. LjeHTp Cl1MM0TPl111 3J1Jlli!nca Ha3blBaeTC!I "eHTPOM 3n- nMnca. np!!Ma!I X = -d Ha3blBaeTC!I AlilP0KTp"1COl1, COOTBBTCTBY- IOlJ.1011 ¢oKycy F,(-c; 0) rAe d = ·~ > a . Hap!IAY c 3TOlii A11P0KTP"1COl1 BBOA!IT np!IMYIO x = d, KOTOpa!I !IBJ1!10TC!I rMnep6ona Mee CBOMCTBa CaoiiCTBO. r11nep6011a 11M00T 40HTP Cli!MMeTp1111. LjeHTP Cl1MM9TPl11i1 r11nep60Jlbl Ha3bl83IOT 40HTPOM ntnep- 6onbl. Caoiicm o. r11nep6011a nepeceKaerc!I c np!IMOl1 y =kx nplA lkl< gBABYX TO'IKax. Ecn11 1"1~ i TO 061J.111X TO- 'leK y npsiMolii 11 r11nep6onb1 Her. To'iKl1 F, (-c; 0) 11 F1 (c; 0) Ha3b1sat0TCS1 itioKycaMM rM- nep6onb1. 3,11ecb c= Ja2 +b2 • 'ieM M0HbW0 3KC4eHTPl1Cl1T0T, T0M 6onee r11nep6011a ClKaTa KOCl1 Ox. n 6 ~apa ona Mee CBOMCtBa CaoiiCTBO. napa6011a pacnonoJKeHa B nonynnOCKO- CTlil X :i: 0. TO'IKY (~, o) Ha3b1Ba!OT ltJOKYCOM napa6onbl 11 0603Ha- YalOT 6yKsolii F n p - P!IMa!I x = -2 8 KaHOHl1'leCKOlil Cll1CT0Me KOOp,1111HaT CaoiiCTBO. napa6ona "1M00T OCb C11MM0TPl11i1. Ha3b1Ba8TC!I AMP0KTPMCOii napa6onbl. PaccTO!IH110 OT Hee Ocb Cl1MMeTp1111 HaJbieaerc!I ocbio napa6onb1. TOYKa ne- AO¢ oKyca Ha3b1saercS1 itioKanbHblM napaMeTpoM napa60- peceYeH1111 napa60llbl c OCblO H33blB38TC!I aepwMHOii na- Jlbl. 0'leBl1AHO, OH paeeH p. 3Kc4eHTP"1Cl1T0T napa60flbl no pa6onbl. Bepw11Ha napa60Jlbl BKaHOHl1'i0CKOlii Cl1CT0Me onpBABJlBHlillO no11arat0T paBHblM BAl1H114e, TO eCTb e=1. KOOPAl1Har HaXOAMTC!I e HaYane KOOpA11HaT. Tenepb csoliicrso, 'lepe3 KOTopoe Mbl onpe.11en11n11 napa- '°iaCTb 3 A11P0KTPlilCOlii, COOTB0TCTBYIOIJ.l0McPOKycy Fi(c; 0). nyCTb M (x,, y,) - TOYKa 3J1Jll10Ca, TOfAa ypaBH0HM0 Ka- carenbHOii K3MMncy B AaHHOM TO'IK0 11MeeT 811A'. x,x + YtY =I a 2 bi . YcnoaMe KacaHMA np11Moii y = mx+k , xi y· . 1i1 3nnMnca 2 + 2 =I . a b k2 = 1n2a 2 +/fl. y bD M A Fi d -a -c 0 c -b c B a d X 0603Ha'ili!M d = ~ ' TO, OOCKOllbKY AJl!I r11nep60llbl e >1, li!M88M d <a. np!!Ma!I x =d Ha3blB38TC!I AMP0KTPMCOii r11nep60nbl, COOTBBTCTBYIOUIBlii cfJOKyCy fj. np!IMYIO X = - d Ha3blB3IOT AIAPBKTPl1COlii, COOTBBTCTBYIOUIBlii ¢oKycy F,. 811,11 r11nep6011b1 11 ee ,1111peKrp11c s KaHoH11YeCKOlii c11cre- Me Koop,1111HaTnp1i1ee,11eH Ha p11c. y -c -d d c x 6ony, s HOBblX TepM1i1Hax MOlKHO ccpopMyn11poearb cne- .llYIOIJ.ll1M o6pa30M: lll06a!I TO'!Ka napa60llbl paBHOYAane- Ha OT ee cpoKyca Iii AIApeKTpl1Cbl. B11A napa6011b1 a KaHoH11YecKolii c11creMe KoopA11Har 11 pacno110JKeH11e ee A11peKrp11cb1 np11seAeHbl Ha p11c. y M -p/2 I~ x -
• ' nonstpHaSI CMCTeMa KOOPAHHaT craBllT BCOOTBeTCTBMe KID!(J011 TO'lKe Ha OJlOCKOCTM napy 'll1Ce11 (p; <p). 0CHOBHblMl1 OOHSIT11SIMH 3TOM Cl1CTeMbl SIBJlSllOTCSI TO'iKa OTC'leTa - nonioc - 11 ny'i, Ha'l11Hat01J.11111CSI B3TOH TO'iKe, - nonstpHaSI OCb. KOOPAMHaTa p - paCCTOSIHl1e OT TO'iKM.110 nonioca, KOOPA11Hara <p - yron Me)l(AY nonsipttol1 OCblO 11 orpe3KOM, coe.a11HS1t0- l1MM nont0c 11 paccMarp11saeMyio TO'iKY, KOropb1i16epercsi co 3HaKoM «+», ecn111 yro11 or oc11 AO orpe3Ka Bb1'111c11S1ercS1 npor11s 'lacosoi.1 crpenK11, 11 co 3HaKoM «-» s npor11sono- no)l(HOM cny'iae. Ba)l(HO noH11MaTb, 'iTO Y11cno <p Bnonsipttoi.1 c11creMe onpe.aeneHOHe OA- H03Ha'lHO: napaM 'i11cen (p; cp +2nn) coorsercr syer OAHa 11 ra)Ke TO'lKa np11 n106b1x Ha- rypanbHblX n. .Qnsi nont0ca p = 0, ayron cp He onpe.aeneH. 150° 180° 210° 120° goo .. 240° 270° 60° ..........__(p .... 300° nonRpHafl CHCTeMa KOOP,QHH8T. 30° 330° nonS!pHble KOOPA11HaTbl nerKO npeo6pa30BaTbB,fleKapTOBbl. nycTb (~; y) - KOOPAl1HaTbl TO'lKl1 BJl0Kaproaol1 Cl1CTeMe KOOPA11HaT, (p; cp) - BnonS!pHOl1. Tor.Qa { x =pc~scp, y = pstncp. <l>opMynb1o6parHoro nepexo.aa: p = Jx2 +y2, <p = arctg ~, x ;t: 0, 1t m=- x= O y> OT 2 ' ' ' 1t tn = - - x= O y< OT 2 ' ' . QMnMHAPH'leCKaA Hcc1JepM'leCK3A CHCTeMbrKOOPAHH3T~ - , . ~ Ha p11cyHKe noKa3aHbl 411n11HAPl1'iecK11e p, <p, z 111 c¢ep111YeCK111e Koop.Q111Harb1 r, fl, <p (nonsipHb1i:1 pa.a11yc, w11pora 11 .Qonrora). z z ......._ .._ .._ '-............ M., (} r 0 y I / cp p : /// y . I / - - --·-- - -- --_../ M' p=.Jx1+y2 , x=pcoscp tg<p = ~ , y = psihcp z =z z cos<p= / , y=rSin0coscp "IJX2+y2+z2 ta1n = Y z = rcos0e ·'t' ~t , AeyrpaHHblHyron - 3TO 'iaCTb npocrpaH- a crsa, 3aKnt0YeHHaS1 Me)l(JlY ABYMRnony- B nnocKocrstM11, 11Met01J.1111M11 OAHY061J.1YIO A ...-------(3;.. rpaH11uy. nonynnocKocr111 o. 11 ~. o6pa3Yt01.ll11e .asyrpaHHbli.1 yron, Ha3b1sat0rcS1 ero rpaH11- MM. 06U,aSI npsiMafl 3Tl!1XrpaHei1 Ha3blBaeTCR pe6pOM AByrpaHHOfO yrna. nycTb TO'iK11 A11 B B3RTbl Ha pe.6pe AByrpaHHoro yrna. .QsyrpaHHbli'.1 yron o6o3HaYaercl! ABYMSI 6yKBaM111 yron AB. TpexrpaHHblH yron OnpeAeneHMe: TpexrpaHHbli'i yron - aro YaCTb npocrpaHcrsa, orpaH11YeHHast rpe- MR nnocK11M11 yrnaM11 c o6u.iei:1 sepw11- HOl1 11 nonapHo 061J.111M11 cropoHaM11, He ne>Kallll1Mlll B0.QHOH nnOCKOCTl1. 061J.1aS1 sepw11Ha 0 3r11x yrnos Ha3b1saercsi eep- WMHOi'i rpexrpaHHoro yrna. CropoHbl yr- c a nos Ha3b1saiorcsi pe6paMM, nnocK11e yrnb1 np11 sepw11HerpexrpaHHoro yrna Ha- 3b1Baiorcsi ero rpaHAMM. rpaH11 rpexrpaHHoro yrna 06pa3yior AByrpaHHbJe yrnb1. TeopeMa «HepaeeHcreo rpeyronbHMKa AJlA rpexrpaHHoro yrna»: Ka>K.Qb1l1 nno- CK11!1 yron rpexrpaHHoro yrna MeHbwe cyMMbl .asyx Jlpyr111x ero nnocK11x yrnos. TeopeMa: a + y + ~ <360°. .QpyrlllMlll CJlOBaMl1, CYMMa nnOCKlllX yrnO,BrpexrpaHHOfO yrna MeHbWe 360°. TeopeMa "TeopeMa KOCMHycoe AJlA rpexrpaHHoro yrna»: cosa= cos 13 cosy + sin 13 siny cos A , fA9 a, f3,y - nnocK11e yrnbl, A - ABYri}aH- Hbllli yron, cocrasneHHbli1 nnocKOCT5lMl1 yrnos f3 11 y. 3aMe'l3HMe. cnoMOUblO A0Ka3aHHOi1 reopeMbl MQ)!(HOBbl'll1Clll1Tb aenl1'il1HY .asyrpaHHoro yrna, 3HaH nnocK111e yrnbl rpexrpaHHOro yrna: A - cos(x - cosf3cosy cos - . (.l • sin ..,siny Ecn111 rpaH11 n11ocK11x yrnos s3a11tMHO nepneHA11KynstpHbl, nony'laeM cpopMyny rpex KOC11Hycos: cos a= cos~ cosy TeopeMa «TeopeMa CMHycoe AflA rpexrpaHHoro yrna»: sina sin f3 srny Cnpase.Qn11so paseHcrso . A = . B - . C Slll SID SH'l fAe a, ~. y - nnocK111e yrnb1 rpexrpaHHoro yrna; A. B, C- npor11so11e)l(au.i11e 11M AByrpaHHb1e yrnb1. OnpeAeneHMe: HecKOnbKO.nnocK11x yrnos c 061.lll1M Ha'i~noM 0, 113 KOTOPblXH11- KaK11e ABa He ne>KaT BOJlHOti nnOCKOCTl1, o6pa3ylOTMHOrorpaHHbli'i yron. 3Tlll nnocK111e yrnbl np11 aepw11He MHOrorpaHHoro yrna Ha3b1saiorcsi rpaHAMM, acropo- Hbl 3r11x yrnos - pe6paMM, roYKa 0 - eepwMHOi'i MHororpaHHoro yrna. no ~11c11y rpaHei:1 MHororpaHHblHyron Ha3b1saerc51 rpexrpaHHblM, YeTb1pexrpaHHblM111 T.Jl. Ecn11 see rpaHIA MHOfOfi}aHHOfO yr11a HaXOJlSITCSI c O.QHOl1 CTOPOHbl OT Ka>KAOlli 1113 nnOCKOCTei.1 ero rpaHei:1, yron Ha3blBaeTCSI BblOYKJlblM. TeopeMa: Ka>t<Jlbli1 n11ocK11i1 yron MHororpaHHoro yrna MeHbwe cyMMbl scex oc- ranbHblXero nnocK11X yrnos. TeopeMa: CyMMa nnocK11x yrnos Bb1nyKnoro MHororpaHHOro yrna MeHbWe 360°. li1H<J>OpMa41<10HHO-CnpaeoYHaS1 Ta6ni.14a © 000 "111Hcj:Jonnacr•., 2006 r. MocKsa, Kaw"'pcKoe wocce, 21 E- mail: mail@infoplast.ru, http://www.infoplast.ru Ten.: (095) 320- 94-89/88 no.am1caHO 8 ne48Tb 28.'12.05. T11paJ1<4000 3K3. 3aKa3 N'1 3106. /13,aarenb 0 00• l1H,Ponnacr•, MOCKBa, Kaw11pCKOe wocce, 2 1. Tunorpa<JJMR 000 «81<ea-C1ap•, 107023, MOCKBa. y11. 311eK-1po3aeo,acKaR, 20 -
napannenbHOCTb npAMOit MnnDCKOCTM OnpeAeJleHMe. npHMaH 11 nnDCKOCTb Ha3blBalOTCH napannenbHbfMM, ecn11 OHl1 He 11MelOT 06lJ111X TOYeK. Ecn11 npHMaH a napannenbHa nnocKo- crn a, TO n11wyT alla. TeopeMa. "npM3HaK napannenbHOCTM npAMOii MnnocKOCTM». Ecn11 npHMaH BHe nnocKocrn napan- nenbHa KaKOiii-Hl16YAb npHMOiii Ha nnocKOcrn, TO 3Ta npHMaH napan- nenbHa 11 caMoiii nnocKOcrn. TeopeMa. TeopeMa ocneAe. Ecn11 nnocKOClb f3 npoXDAl1l Yepe3 npHMYIO a, napannenbHYIO nnDCKO- fl a PMCYHDK 1. a - HBKOTOpaH nnoCKOCTb, I - HB ne>Ka- L11aH e JTOii nnocKocrn npHMaH, /, - npH- MaH e nnocKocrn a, napannenbHaH !. cm a, 11 nepeceKae1 3lY nnocKOClb no npHMDiii b, TO blla. OnpeAeneHMe. npHMYIO b 11HDrAa Ha3b!BalOT cneAOM nnoCKOCTM /3 Ha nnDCKOCrn a. napannenbHOCTb ABYX nnDCKOCTeit OnpeAeneHMe. Ase nnocKocrn Ha3bl- sa10lCH napannenbHbfMM, ecn11 0H11 He 11MelOT 06U111X TOYeK. TeopeMa. «npM3HaK napannenbHOCTM nnOCKOCTeii». Ecn11 ABe nepeceKa10lJ111ecH npHMble DAHOiii nnocKOCTl1 COOlBelCTBeHHO napannenbHbl ABYM npHMblM APYrDiii AoKa3aTeJ1bCTBO. nposeAeM s AaH- HOiii nnOCKOCTl1 p KaK11e-n1160 ASe ne- peceKalOlJ111eCH npHMble a 11 b. Lfepe3 TOYKY A nposeAeM napannenbHble 11M npHMble a, 11 b,. nnocKOClb P,, npo- XOAHlJ1aH Yepe3 npHMble a, 11 b,, na- pannenbHa nnocKocrn P. AonycrnM, YTO Yepe3 TOYKY A npoxo- nnocKOCTl1, TO 3111 nnocKocrn napan- A11l APYraH nnocKOClb P,, TO>Ke na- nenbHbl. pannenhHaH nnocKoc111 P. 01Me111M Ha Heiii KaKyl0-111160 TOYKY C, He ne- PMCyHOK 2. P, ~ P, - 11aHHb1e nnocKocrn; a, ~ a, - npHMblB e nnocKOcrn P,, nepece- Ka10L11~ecH BTOYKB A; b, ~ b, - COOTBBTCTBBHHO napa11nenbHblB ~M npHMblB BnnocKDcrn P,. TeopeMa. Ecn11 ABe napannenbHble nnocKocrn nepeceYeHbl TpeTbeiii, TO OHa OCTaBJlHel Ha 3Tl1X nnocKOCTHX napannenbHble cneAbl. TeopeMa. Lfepe3 TOYKY BHe AaHHOiii nnocKocrn MD>KHD nposecrn nnoc- KDCTb, napannenbHYIO AaHHOiii, 11 np11- TOM TOJlbKO DAHY. A~7 ~~b/ >Kal!1yl0 s nnocKocrn P,. nposeAeM nnOCKOClb a Yepe3 TOYKl1 A, c 11 Ka- KYI0-111160 TOYKY B nnOCKOCTl1 P. nnocKOClb a nepeceYeT nnocKocrn P, P, 11 P, no npHMblM b, a 11 c. npH- Mb1e a 11 c He nepeceKalOT npHMYIO b, laK KaK He nepeceKalOT nnocKOClb P. CneAOSaTenbHO, 0H11 napannenbHbl npHMOiii b. Ho s nnocKocrn a Yepe3 TOYKY A MO>KeT npOXOAl1Tb TOJlbKO OAHa npHMaH, napannenhHaH npH- Moiii b. nonyYeHo npornsopeY11e. TeopeMa. 01pe3Kl1 napannenbHblX npHMblX, orpaH11YeHHb1e ASYMH na- pannenbHblMl1 nnoCKOCTHMl1, paSHbl. TeopeMa. Asa yrna c cooTseTCTseHHO napannenbHblMl1 11 OA11HaKoso Hanpa- sneHHblMl1 CTOPOHaMl1 paSHbl 11 ne- >KaT BnapannenbHblX nnOCKOCTHX. OnpeAenett11e. npHMaH Ha3b1sae1cH nepneH- Ha3b!SaeTCH 0Tpe30K npHMOiii, nepneHA11KY- IJMKynRpHoft nnoCKOCTl1, ecn11 OHa nepneHAl1- nHpHoiii AaHHOiii nnoCKOCll1, KOTOpbliii COeA11- KynHpHa Jll060iii npHMOiii 113 3TOiii nnoCKOCTl1. TeopeMa. «npM3HaK nepneHAMKynApHOCTM npAMOii MnnocKOCTM». Ecn11 npHMaH nepneHA11KympHa Ka>KAOiii 113 ASYX nepeceKalOlJ111XCH npHMblX nnocKOCTl1, TO OHa nepneHA11KynHpHa 3TOiii nnOCKOCTl1. PMCyHOK 4. a a - npHMaH, nepnBHA~KynHpHaH npffMblM b ~ C, ne>Kalll~M BnnocKocrn P ~ npHMaff a npoxo11~T Yepe3 TOYKY A nepeceYeH~H npHMblX b ~ c nnoc- Kocrn P. TeopeMa. nnocKOCTb, nepneHA11KynHpHaH OA- Hoiii 113 ASYX napannenbHblX npHMblX, nepneH- Al1KynHpHa 11 APYrDiii. TeopeMa. Ase npHMble, nepneHA11KynHpHble OAHDiii nnoCKOCTl1, napannenbHbl Me)l(Ay co- 6oiii. TeopeMa. Ecn11 npHMaH nepneHA11KynHpHa OAHOiii 113 ASYX napannenbHblX nnoCKOCleiii, TO oHa nepneHAl1KynHpHa 11 APYrDiii. TeopeMa. Ase nnocKoc111, nepneHA11KynHp- Hble OAHOiii npHMOiii, napannenbHbl Me>KAY co6oiii. OnpeAeneHMe.nepneHIJMKynRpoM, nposeAeH- HblM 113 AaHHOiii TOYKl1 Ha AaHHYIO nnOCKOClb, HHeT AaHHYIO TOYKY c TOYKOiii nnOCKOCll1. TeopeMa. Ecn11 113 OAHOiii TOYKl1 SHe nnoCKO- CTl1 nposeAeHbl KHeiii nepneHA11KynHp 11 Ha- KnOHHble, TO: AJ111Ha nepneHAl1KynHpa MeHhwe AJ111Hbl nl06oiii HaKnOHHOiii; • HaKnOHHble c paSHblMl1 npoeKljl1HMl1 paSHbl; • 113 ASYX HaKnOHHblX 60J1bWYIO AJ111HY 11Meel Ta, y KOTOpoiii 6onbwe npoeKljl1H. TeopeMa. «O rpex nepneHAMKynApax... Ecn11 npHMaH, npoBeAeHHaH Ha nnocKOCTl1 Yepe3 OCHOSaH11e HaKnOHHOiii, nepneHA11KY- nHpHa ee npoeK111111, TO OHa nepneHA11KYnHP- Ha 11 caMoiii HaKnOHHOiii. nycTb AC- HaKnOHHaH npHMaH KnnocKo- cT11 P, BC- npoeKl111H npHMoiii AC Ha nnoc- KOCTb P, T.e. BCE P, npHMaH BC nepneHA11- KynHpHa npHMOiii /, ne>KalJ1eiii s 3TOiii nnOCKO- CTl1. Tpe6yeTCH AOKa3alb, YTO HaKnOHHaH AC TaK>Ke nepneHA11KynHpHa npHMoiii I. PMCyHOK 5. p TeopeMa (o6paTHaA). Ecn11 npHMaH Ha nnoc- Koc111 nepneHA11KynHpHa HaKJlOHHOiii, TO OHa nepneHA11KynHpHa 11 npoeKljl111 HaKnOHHOiii. nycTb /..L CA, IE P, Tpe6yeTCH AOKa3aTb, YTO / ..L CB, rAe CBE P 11 HBnHeTCH npoeK1111eiii npHMOiii CA Ha nnocKOCTb P. nepneHAMKynApHDCTb ABYX nnocKocreit OnpeAeneHMe. Jiae nepeceKalOU111ecH nnocKo- cr11 Ha3blBalOlCH nepneH/jMKYflflPHblMM, ecn11 lpelbH nnocKOClb, nepneHA11KynHpHaH npH- Moiii nepeceYeH11H a111x nnocKocreiii, nepece- Kae111X no nepneHA11KynHpHblM npHMblM. TeopeMa. «npM3HaK nepneHAMKynApHOCTM ABYX nnocKOCTeii». Ecn11 nnocKOCTb npoxDA11T Yepe3 npHMYIO, nepneHA11KYnHPHYIO APYrDiii nnocKoc111, TO 3111 nnocKOCll1 nepneHAl1KYl1HpHbl. PMCyHOK 6. a- npHMaff, nepneHA~KynHpHaff nnocKOcrn P; P, - nnocKOCTb, npoxOAfflllaff Yepe3 npHMYIO a; TeopeMa. Ecn11 nnocKOCTl1 a 11 f3 s3a11MHO nepneHA11KYl1HPHbl, 11 KnnOCKOCTl1 a npose- AeH nepneHA11KynHp, 11MelOlJ111iii 06U1YIO TOYKY c nnoCKOClblO /3, TO 3TOT nepneHA11KynHp ne- >Kl1T BnnoCKOCll1 /3. TeopeMa. nycTb nnocKocT11 a 11 f3 nepneHA11- KynHpHbl nnOCKOCTl1 y 11 nepeceKalOlCH no npHMOiii a, TOrAa a ..Ly. a A b c p P, b - npffMaH, no KOTOpoii nepeceKalOTCff nnoCKOCTH p Hp . noKaJaTb, YTO nnOCKOCTH PM P nepneHJ)~K}'JlffPHbl _J
OnpeAeneHMe. 06~HM nepneHAHKynRpoM ABYX CKpe~HBa/O~HXCR npRMb/X Ha3blBa- eTeR oTpe3oK e KOHL1aM11 Ha arnx npRMblX, nepneH,Ql1KYl1RpHblH Ka)f(,!OH 113 arnx npR- MblX. TeopeMa. ,Qse eKpeU11Ba10Ul1ee11 np11Mb1e 11MelOT 06U11H nepneH,Ql1KYl1Rp, 11 npMTOM e,Q11HeTBeHHblH. JleMMa. ,Qse eKpeU11Bat0U11ee11 np11Mb1e 11e>KaT Bnapa1111e11bHblX n11oeKoeT11x. OnpeAeneHMe. YrnoM MeJKAY HaKnoHHofl H nnOCKOCTb/O Ha3blBaeTeR yra11 Me)f(,!ly Ha- K110HHOH 11 ee opTOraHanbHOH npoeKLjl1eH Ha n11oeKOeTb. TeopeMa 06 061QeM nepneHAMKym1pe ABYX CKpe1QHBa101QMXCA npAMblX 0 a Ha p11cyHKe 7 noKa3aHa HaK110HHa11 AB, OB = IlpaAB, LABO- yra11 Me)f(,!ly Ha- Kl10HHOH AB 11 n11oeKoeTbt0 a. Ee1111 np11- Ma11 napan11e11bHa n11oeKoern, TO yra11 Me- >KAY Hl1MM no onpe11e11eH11t0 pa- seH 0°. Ec1111 np11Ma11 nepneH,Ql1KY- 11RpHa n11oeKoern, TO yra11 Me)f(,!ly Hl1Ml1 paseH go0 . Ee1111 {3- yra11 Me)f(,!ly npRMOH 11 n11oeKOCTblO, TO 0°< f3 < go0 • npose,QeM S n11oeKoern a npo113so11bHY10 npRMYIO b Yepe3 TOYKY B TaK, YT0- 6bl ocj_ b. nym LABO = {3, LOBC = y, LABC = <p. PaeeMaTpl1BaR np11Moyra11bHb1e Tpeyra11bH11K11 ABO, OBC, ACB, 11MeeM OB BC BC cosl3 =AB , cosy= OB , coscp = AB · . BC OB BC 3aMernM, YTO. AB = AB . OB 111111 coscp =cos 13 ·cosy . Mbl no11yY111111 ljJopMyny rpex KOCMHYCOB. 06parnre BH11MaH11e Ha TO, YTO n11oeKoern yrnoB f3 11 y B3al1MHO nepneH,Ql1KYl1RPHbl. 3aMe'laHMe. noeKOl1bKY yrnbl <p, f3 My OCT- pb1e, 113 cpopMyl1bl Tpex Koe11Hyeos e11e11y- eT, YTO cosl3 > coscp 110° <13 <cp . TaK11M o6pa30M, yrnoM f3 Me)f(,!ly HaK110H- HOH Mee opTOraHanbHOH npoeKLjl1eH Ha n11oeKOeTb RBl1ReTCR Hal1MeHbW11H 113 yr- 1108, o6pa30BaHHblX HaKl10HHOH e npRMbl- MM n11oeKoern a. DapannenbHOCTb npAMblX OnpeAeneHMe. napa1111e11bHOe npoeKrnposaHMe, npM KOTOPOM npoeKrnpylOUMe npRMble nepneH,QMKy1111pHbl Kn11oeKoern npoeKLjMH, Ha3blBaeTeR oproroHanbHb/M npoeKTHPOBaHHeM. OnpeAeneHMe. ,Qse np11Mb1e BnpoeTpaHeTBe Ha3b1Bat0Te11 napannenbHblMH, ee11M OH1111e>KaTB0.QHOH n11oeKOeTM 11 He MMelOT 06U11XTOYeK. OnpeAeneHMe. npRMble, KOTOpble He MMelOT 06U11XTOYeK 11 He napan11e11bHbl, Ha3blBalOTeR CKpe~HBa/O~HMHCR . 3aMe'laHMe. CornaeHo onpe11e11eHMIO, .QBe napan11e11bHb1e npRMble 11e>KaT BOAHOiii n11oeKoern. nerKo 3aMernTb, YTO Yepe3 .QBe napan11e11bHb1e np11Mb1e MO>KHO nposee- rn TOl1bKO OAHYn11oeKOeTb. TeopeMa. n110Ua.Qb opTOraHa11bHoi1 npoeKL111M MHora- yra11bH11Ka Ha n11oeKOeTb pasHa npOM3Be,QeHMIO era nl10Ua.QM Ha KOeMHye yrna Me>KAY n11oeKOeTblO MHOra- yral1bHMKa Mn11oeKoeTbt0 npoeKLjMM: Sap= S coscp . MHororpaHHHKOM BTpexMepHOM npo- CTpaHCTBe H83blBaeTeR COSOKynHOCTb KOHeYHOro '111e11a n11oeKl1X MHoroyro11b- Hl1KOS TaK3R, 'ITO: • K3)f(,!1311 CTOPOHa 11t06oro 113 MHOro- yro11bHl1KOS eeTb O,QHospeMeHHO eTopo- Ha APYraro (HO TOl1bKO OAHOro), H33bl- saeMoro cMe>KHblM e nepeblM no 3TOM eTopoHe; TeopeMa. '-lepe3 TOYKY BHe ,QaHHOH npRMOHMO>KHO npo- seern npRMYIO, napan11e11bHYIO ,QaHHOH, Mnpl1TOM TOl1b- KO OAHY. OcHOBHble noHATMA TeopeMa. «npM3HaK cKpe111Meaio111MxcA npAMblX». Ee11M O.QHa M3 ABYXnpRMblX11e>KMT Bn11oeKoern, a 11pyra11 nepeeeKaeT 3TY n11oeKoeTb BTOYKe, He np11Ha,Q11e>Kalleiii nepsoiii npRMOH, TO am ABe npRMble eKpeUMBalOTeR. pan11e11bHblXn110CKOeTllX, Ha3blBaeTell npH3MaTOHAOM. npH3Ma, nHpaMHAa Hyce~eHHaR nHpaMH- Aa - 'laeTHble e11y'la11 np11aMaT011Aa. Bee 60KOSble rpaHl1 npM3M3TOl1,Qa 11811lllOTCll Tpeyro11bH11KaM11 111111 '1eTb1pexyra11bHMKa- M11, np11'leM 'leTb1pexyra11bHb1e rpaH11 - 3TO Tpanelj1111 111111 napan11e11orpaMMbl. • OT 11t06oro 113 MHorayrOl1bHl1KOB, eocTa- e1111t011111x MHOrorpaHHl1K, MOlKHO AOMrn AO 11t06ora 113 H11X, nepeXOAll no O'lepe- Al1 OT 0.QHOro MHOrayrOl1bHMKa K.Qpyra- My, CMelKHOMy CHMM. MHorayrol1bHHKl1, 113 KOTOpblX eoCTOllT MHOrarpaHHMK11, H33b1Bal0Tell rpaHRMH, MX CTOPOHbl - pe6paMH, a HX BBPWMHbl - BepWHHaMH MHOrorpaHHHKa. Ha p11cyHKe 8 np11ee.QeHbl HeKoTOpb1e np11- Mepb1 MHOrorpaHHl1KOB. OnpeAeneHMe. MHorarpaHHl1K Ha3b1eaeTc11 BblnYKflblM, ee1111 OH 11e>KMT no OAHY eTO- poHy OT n11oeKOeTM 11I060M era rpaHM. Illa aTOro onpe11e11eHM11 e11eAyeT, YTO see rpaHM BblnYKllOro MHOrorpaHHMKa llSl111- IOTCll n11oeKl1MM BblnYKl1blMM MHoroyro11b- HMKaMM. noeepxHOeTb BbmyK11ora MHOro- rpaHHMKa eoeTOMT M3 rpaHeM, KOTOpb1e 110- >KaT Bpa3HblX n11oeKOeTllX. npM 3TOM pe6- paMM MHOrorpaHHMKa 11811lllOTell eTOpOHbl MHOroyrOl1bHMKOB, sepwMH3MM MHOra- rpaHHMKa - sepwMHbl rpaHeM, n110CKl1MM yrnaMM MHOrorpaHHMKa - yrnbl MHOro- yral1bHl1KOB-rpaHeM. TeopeMa CMMOCOHa. 06b8M vnpl13MaTOl1,Qa MO>KHO Hai.irn no I cpopMy11e: V =- H(S1+4S+S2), 6 r.Qe H - era SbleOTa (paeeTOllHMe Me)f(,!ly n11oeKOeTllMl1 oeHOB3HMH), S, 11 S, - n110- Ua.Ql1 oeHOBaHl1M, s- nl10Ua.Qb cpeAHero ce~eHHR (eeYeH1111, napan11e11bHOra n11oe- Koer11M oeHo~aHMH 11 ,Qe1111Uero BbleOTY nono11aM). OnpeAeneHMe. BbmyK11blM MHorarpaHHMK, see sepwMHbl KOTOpora 11e>KaT s ABYX na- OnpeAeneHMe npaaMnbHoro MHororpaHHMKa Cpe,QM n11oeKl1X MHOrayra11bHMKOB oeo6oe Mecro 3aH11Ma10T npas1111b- Hb1e MHorayra11bH11K11. Cy111eeTsy10T 1111 «npas1111bHble MHOrarpaHH11Kl1», 11 'ITO 3TO TaKOe? Ellie B,QpesHeM rpeljl111 6bll111 M3BeeT- Hbl n11Tb YA11SMTel1bHblX MHorarpaH- H11KOB. OnpeAeneHMe. MHorarpaHHMK Ha3bl- eaeTe11 npaBHflbHblM, ee1111 see era rpaHM - paeHble Me)f(,!ly eo6oi1 npa- s1111bHb1e MHOrayra11bHl1Kl1, M3 Ka>K- AOM era sepWl1Hbl SblXOA11T OA11H3KO- BOe '111e110 pe6ep 11 see 11syrpaHHb1e yrnb1 pasHbl. TeopeMa. CyUeeTsyeT He 6011ee n11TM pa311H'IHblX BM.QOB npaSl111bHblX MHO- rarpaHHl1KOS. npaBMftbHble MHOrorpaHHMKM. 06o3Ha'leH1111: a - pe6po, H - sb1eo- Ta, s- nl10Ua.Qb noeepXHOeTH, v- o6beM, R- pa1111ye on11eaHHOH ecpe- pb1, r- pa.Q11ye en11eaHHOH ecpepbl. <l) @Ky6. Bee weeTb rpaHeH - Terpa3AJ1. Bee YeTb1pe 01T33AP. Bee BOeeMb Aone1a3np. Bee 12 rpa- MIOC33AP. Bee 20 rpa- KBil,lpaTbl. 111MeeT soeeMb rpaHH - paBHOeTOpOHHHe rpaHeH - paBHOeTOpOH- HeH - npasHnbHb1e n11rn- HeH- paBHOeTOPOHHHe sepwHH H12 pe6ep. TpeyronbHHKH. 111MeeT HHe TpeyronbHHKH. yronbHHKH. 111MeeT TpeyronbHHKH. 111MeeT YeTb1pe sepwHHbl H 111Meer weeTb sep- 20 sepwHH H30 pe6ep. 12 BepWHH H30 pe6ep. weeTb pe6ep. WHH H12 pe6ep. R =!!..J3 2 R= !!..J6 4 R =!!.J2 2 R =* (1+J5) .J3 R =* J 2(s+ J5) a r =I~ .J6 r =!!..J6 a R r =--Y.;-(3+J5)r= - r =4' 10+~2 6 ·d 4d S =6a2 S = a'.J3 S = 2a' .J3 S = 3a5(5~2d) S=5a' .,.3 V=a' a' re V- a' -:i-V=u..,2 11· a' t--=-== I ' - :a' (' :)- 3 , _ ==~ ,.: )- , ... -~ ~- I• nyeTb SA,A, ... A, - npaBMl1bH311 n-yral1bH3R nt1pa- Ml1,Qa. Bse.QeM e11e.QYIOUMe o6o3HaYeH1111: • a - yra11 HaKl10Ha 60KOSOra pe6pa Kn11oeKOeTM oe- HOBaH1111; {3- ,QByrpaHHblH yra11 np11 oeHOSaH1111; • y- n11oeKMi1 yra11 npM sepw11He; • 0 - ,QByrpaHHbliii yra11 np11 60KOSOM pe6pe. Tor,Qa enpaBeAJ111Sbl eOOTHOWeH1111: tga =cos*·tg13; sin l cosa= - -2 · . n ' sm 2 sina= ctg* ·ctg~ ; cos 13 =ctg-Ji- ·tg1 ; y cos-Ji- cos_§_ cos - = --· sinl3 =--2 2 sin_§_ ' sin-J} · 2 l1Hcf>OpMa1.1110HHO-cnpaeo<1HaR rn611111.1a ""0 0
HH4'0n/ACT TM www.infoplast.ru nyTeBOAMTellb no 'f8CTR M p e'fM --------.....lr1M~ CylleCTBLitTe/lbHOe 8HMMaH11e! Bee eyl4eeTs1.nenbHb1e B HeMe4KoM Sl3b1Ke n111wyTeSl e 3arnaBHOl1 6yKBbL. HeMe4K111e eyl1jeeTBlllTenbHble eKnOHSllOTefl no YeTbLpeM naAe>KaM. Cyl4eeTBlllTenbHoe B 111MeH111TenbHOM naAe>Ke (Nominativ) eny>1<111T B npeAnO>KeH111111 noAne>KaL4111M, B BlllHlllTenbHOM (Akkusativ)- npSlMblM 111n111 KOeBeHHbLM AOnonHeHllleM, B AaTenbHOM (Oativ) - TOnbKO KOeBeHHbLM AOnonHeHlll- eM. PoA111TenbHb1l1 (Genitiv) naAe>K o6o- 3Ha'-LaeT np111HaAne>KHOeTb; eyl4eeTBlllTenb- HOe B POAlllTenbHOM naAe>Ke, KaK npas111no, eny>1<111T B npeAnO>KeH111111 onpeAeneH111eM. POA HeMe4K111e eyl4eeTB111TenbHb1e 6b1sa10T My>KeKoro, >KeHeKoro 111 epeAHero POAa. noKa3aTeneM POAa eny>1<111T onpeAeneH- HbLl1 aprnKnb der (M.), die (>K.), das (e.). K JKeHCKOMY POAY. KaK npae1mo, OTHO- CRTCR cy1.1.1ecTBMTenbHble: 1.06o3Ha'-LalOL4111e n1114 >KeHeKoro nona (B TOM '-Llllene lllMelOL4111e eycpcp111Ke >KeHeKoro poAa - in: die Frau, die Spanierin, die Chemikerin). 2. EionbWlllHerno eyl4eeTBlllTenbHblX, 111Me- 10L4lllX oKOH'-LaH111e -e: die Kirche, die Buehne, die Kontrolle. Cyl4eeTBlllTenbHble, OKaH'-LlllBIOL4111eefl Ha - ion, -heit, -keit, -schaft, -taet, -ung, - ur, -ie, -ik, -enz, -ei, -anz: die Revolution, die Freiheit, die Taetigkeit, die Freundschaft, die Universitaet, die Zeitung, die Kultur, die Demokratie, die Physik, die Konferenz, die Arznei, die Bilanz. K MYJKCKOMY POAY. KaK npae11no, OTHO- CRTCR cy1.1.1ecTBMTenbHble: 1. 06o3Ha'-LalOL4111e n1114 My>KeKoro nona: der Mann, der Junge, der Professor, der Spanier. 2. Cyl4eeTB111TenbHb1e, 06pa3osaHHb1e e noMOL4blO eycpcp111Kea -er OT rnaronos: der Maler, der Schneider, der Lehrer. 3. Ha3BaHlllSl BpeMeH roAa, MBeH4es Ill AHei1 HeAen111: der Sommer, der April, der Sonntag. 4. Cyl4eeTB111TenbHb1e, 0KaH'-LlllBa10L4111ern Ha eycpcp111Ke -en, -ig, -ling, -or, -us: der Ofen, der Honig, der Fruehling, der Direktor, der Kommunismus. K cpeAHeMy POAY 06bl'fHO OTHOCRTCR: 1. EionbWlllHeTBO eyl4eeTBlllTenbHblX, OKaH- '-LlllBalOL4111XeSl Ha eycpcp111Ke -tum: das Christentum. 2. lllHcplllHlllTlllBbl rnaronoB B cpyHKL..1111111 ey- L48eTBlllTenbHOro: das Lemen, das Lesen. 3. Cyl4eeTB111TenbHb1e e yMeHbW111TenbHb1M111 eycpcp111KeaM111 -chen, -lein, a TaK>Ke e eycpcp111KeaM111 -ment, -um: das Kaninchen, das Tischlein, das Monument, das Datum. BHMMaHMe! Cyl4eeTB111TenbHb1e das Maedehen, das Fraeulein, das Weib OTHOef!TeSl K epeAHeMy POAY· MHo>KecTeeHHoe 'fMcno Mtto>1<eeTBBHHoe '-1111eno HeMe4K111x eyl4eeT- BlllTenbHblX 06pa3yeTeSl: ,QnH >KeHeKoro POAa - e noMOl.4blO eycpcp111- Keos -en, -n: die Kirche - die Kirchen, die Uebung - die Uebungen. ,QnH My>KeKoro 111 epeAHero POAa - e noMo- l.4blO eycpcp111KeOB - er, -e. np111 A06asneHllllll eycpcp111Kea -er KOpHeBb1e rnaeHb1e a, o, u, au np111H111Ma10T yMnHyT: der Tisch - die Tische; der Buch - die Buecher. Cyl4eern111TenbHb1e My>KeKoro 111 epeAHero POAa, 0KaH'-L111Ba10L4llleef! Ha -er, He 1113Me- Hfll0Tefl n11160 nplllHlllMalOT yMnflYT B KOpHe: der Bruder - die Brueder; das Fenster - die Fenster. CKnOHeHMe 11MeH cy1.1.1ecTe11TenbHb1X B eAlllHeTBeHHOM '-1111ene pa3n111'-La10T e111nb- Hoe eKnOHeH111e, ena6oe eKnOHeHl!le Ill >KeH- eKoe eKnOHeHl!le. Bo MHO>KeeTBeHHOM '-Lllle- ne see CYL4eCTBlllTenbHble CKnOHSllOTCSl no OAHOMY rnny. CMnbHOe CKnOHeH11e K ClllnbHOMY CKnOHeHllllO OTHOClllTCSl 6onb- WaSl '-LaCTb cyl4eCTB111TenbHblX My>KcKoro POAa Ill Bee - cpeAHero POAa. Maskulinum Neuter Norn. der Lehrer, der Platz das Fenster, das Kind desGen. des Lehrer-s, Fensters, des Platz-es des Kind-es dem Platz dem Lehrer, Oat. dem Lehrer, dem Kind Akk. den Lehrer, den Platz den Lehrer, den Kind Cna6oe cKnoHeH11e K cna6oMy CKnOHeHllllO OTHOCSlTCSl CYL4eCT- BlllTenbHble My>KcKoro POAa, 0KaH'-LlllBa10- L4lllecH Ha -e, a TaK>Ke Ha cycpcplllKCbl lllHO- CTpaHHOro npOlllCXO>KAeHlllSl -ist, -ent, -ad, -et, -nom. BHMMaHMe! Cyl4eCTB111TenbHbie der Held, der Hirt, der Herr, der Mensch, der Baer TaK>Ke OTHOCSlTeSl K cna6oMy CKnoHeHllllO. Norn. Gen. Oat. Akk. der Genosse, der Held des Genossen, des Heiden dem Genossen, dem Heiden den Genossen, den Heiden >KeHCKOe CKnOHeHMe K >KeHCKOMY eKnOHeHllllO OTHOeSlTCSl see CYL4eCTBlllTenbble >KeHCKOro POAa. n3Ae>K- Hble OKOH'-LaHlllSl B 3TOM Tlllne CKnOHeHlllSl OTCYTCTBYIOT. AprnKllb Bee aprnKn111 cornacy10TeH e cyl4eCTB111- TenbHb1M111 no naAe>KaM, POAaM 111 '-LlllenaM. OnpeAeneHHblM apTMKnb ynoTpe6nHeTCSl c 111c'-L111cnHeMb1M111 cyL4eCTB111TenbHb1M111 B eAlllHCTBeHHOM 111 MHO>KeCTBeHHOM '-Llllcne, a TaK>Ke c tte111e'-1111CnHeMb1M111 cyl4eCTBlllTenb- HblMlll. Oni>eAeneHHblM apTMKJlb np111MeHHeTef!, ecm1npeAME!T113aecTeH roaopS1L4BMY. 4BCTb 1 ynoM111HaneH pattee 111n111 HBnHeTCSl BAlllHeT- seHHblM B eaoeM poAe, a TaK>Ke ecn111 ne- PBA eyl4eeTBlllTenbHblM CTOlllT np111nara- TenbHoe B npeBOCXOAHOl1 CTeneHlll lllJllll no- PSlAKOBOe '-L111en111TenbHOe (der beste Schueler, das erste Jahr). HeonpeAeneHHblM apTMKnb ynoTpe6nH- eTCSl TOnbKO e 111c'-L111CnfleMblMlll eyl1jeCTBlll- TenbHblMlll B eAlllHCTBeHHOM '-LlllCne, ecn111 npeAMeT Helll3BeCTeH roBOPSll4eMy. Dort steht ein Maedchen. Das Maedchen ist noch ganz klein. CKnoHeHMe apTMKnelli OnpeAeneHHb1iil apT11Knb My>K. p. >KeH. p. Cp. p. MH. 'f. Norn. der die das die Gen. des der des der Oat. dem der dem den Akk. den die das die Bo MHO>KeCTBeHHOM '-LlllCne aprnKnlll CKnO- HSllOTCSl OAlllHaKoso He3aa111c111Mo OT poAa. HeonpeAeneHHbliil apTMKnb My>K. p. >KeH. p. Cp. p. Norn. ein eine ein Gen. eines einer eines Oat. einem einer einem Akk. einen eine ein JlW·IHble MeCTOLitMeHLit~ n111'-1Hble MeCTOlllMeHlllSl B HeMe4KOM Sl3b1Ke 1113MeHHIOTCSl no naAe>KaM 111 '-LlllCnaM. EA. 'f. ich- fl dU-Tbl er-OH sie - oHa es - OHO Nominativ MH. 'f. wir- Mbl ihr- Bbl (MH.'-Lllleno OT «Tbl») sie - OHlll Sie - Bbl (se>1<n111saH cpopMa) BHMMaH11e! MecrnMett111e Sie, o6o3Ha'-Lal0- L4ee Be>KnlllBYIO cpopMy o6paL4eHlllSl «Bbl», B HeMe4KoM Sl3b1Ke scerAa n111weTcf! c 3a- rnasttol1 6yKBbl, B 0Tn111'-L111e OT pyccKoro, rAe 3arnasttaf! 6yKsa ynoTpe6nHeTCSl TOnbKO B nlllCbMax. ich-meiner du -deiner er- seiner sie - ihrer es -seiner ich- mir du-dir er-ihm sie -ihr es-ihm ich-mich du - dich er - ihn sie-sie es- es Genitiv Oativ Akkusativ wir- unser ihr- euer sie -ihrer sie - lhrer wir - uns ihr - euch sie- ihnen Sie - Ihnen wir - uns ihr - euch sie - sie Sie - Sie
np1maraTe/1bHble HeMe4K1-1e np1-111araTe11bHb1e comacyioTCR c cy1J.1eCTB"1T011bHblM"1 no POAaM, n~ell<aM "1 4"1CllaM. CKnOHeHMe npMnaraTenbHblX Cna6oe cKnoHeHMe, eAMHCTBeHHoe '4Mcno (onpeAeneHHblM apTMKnb) My>K. p. >KeH. p. Cp. p. Nom. der alte Mann die alte Frau das kleine Kind Gen. des a/ten Mannes der a/ten Frau des kleinen Kindes Oat. dem a/ten Mann der a/ten Frau dem kleinen Kind Akk. den a/ten Mann die alte Frau das kleine Kind Cna6oe CKnoHeHMe, MHO)l(eCTeeHHOe '4MCno (onpeAeneHHblM apTMKnb) My>K. p. >KeH. p. Cp. p. Nom. die a/ten die a/ten die Maenner Frauen kleinen Kinder Gen. der a/ten der a/ten der Maenner Frauen kleinen Kinder Oat. den a/ten den a/ten den Maennern Frauen kleinen indern Akk. die alten die alten die Maenner Frauen kleinen Kinder CMnbHoe CKnoHeHMe, eAMHCTBeHHoe '4Mcno: (HeonpeAeneHHblii apTMKnb) My)I(. p. >KeH. p. Cp. p. Nom. ein alter eine alte ein kleines Mann Frau Kind Gen. eines alten einer alten eines Mannes Frau kleinen Kindes Oat. einem alten einer alten einem Mann Frau kleinen Kind Akk. einen alten eine alte ein kleines Mann Frau Kind CMnbHOe CKnOHeHMe, 9AMHCTBeHHOe '4Mcno (6e3 apTMKni:1) Nom. harter Stein rote Jacke frisches Wasser Gen. hartes Steines roter Jacke frischen Wasser Oat. hartem Stein roter Jacke frischem Wasser Akk. harten Stein rote Jacke frisches Wasser CMnbHOe CKnOHeHMe, MHO>KeCTBeHHOe '4MCno (6e3 apTMKnl'I) MyJK. p. >KeH. p. Cp. p. frischeNom. harte Steine rote Jacken Wasser Gen. harten Steines rater Jacken frischen Wasser Oat. hartem Stein rater Jacke frischem Wasser Akk. harten Steinen rote Jacke frisches Wasser npMTl'l>K8TenbHble M9CTOMM9HMl'I np"1TR)l(aTellbHbl0 M0CT0"1M0H"1R comacylOT- CR c cy1J.1eCTB"1TellbHblM"1 no POAaM, n~e- )l(aM .,, 4"1CllaM. ich-mein du-dein er, es - sein, dessen sie - ihr, deren wir- unser ihr- euer sie - ihr, deren Sie- lhr 8HMM8HHe! np1-111araT011bH00 np1-1MaeT n~0)1(Hbl0 OKOH- 4aH"10 C"111bHOrO CK110H0H"1R, 0C11"1 n0p0A H"1M CT0"1T 1110600 npHrnll<aT011bH00 M0CTO- HM0HH0 111-160 OTpH4aT011bH00 M0CTOHM0HH0 kein. n p1o111araT011bH00 npHHHMaeT naA0)1(Hb10 OKOH4aHHR c11a6oro CK110H0HHR, 0C11"1 n0p0A H"1M CTOHT OAHO "13 C110AYIOIJ.1HX yKa3aT011b- HblX M0CT0"1M0H"1iii, H3M0HRIOLJ.HXCR no rnny onp0A0110HHoro aprnK11R: dieser 3TOT jener TOT jeder Ka)l(Abliii mancher H0KOTOpbliii solcher TaKOiii welcher KOTOpbliii r11aro11 HeMe4K1-1iii maro11 H3M0HR0TCR no 111o14aM H 4HCllaM. 11H'4Hbl9 OKOH'48HMl'I rnarona: fA.'4. MH.'4. 1 n. 2n. 3n. -e -st -t -en -t -en 0CHOBHbl0 cj>opMbl maro11a: HHQlHHHTHB, Q>opMa npocToro npoweAwero speMeH1-1 (lmperfekt) H np1o14acrne npoweAwero spe- MeH1-1 (Partizip II). C11a6b1e maro11b1 npHHHMalOT OKOH4aH1-1e -te B lmperfekt H -t s Partizip II: tanzen - tanzte - getanzt sagen - sagte - gesagt C1o111bHb10 maro11b1 1-1Me10T 4ep0AOBaH1o1e KOpH0BblX maCHblX B pa3HblX Q>opMax ... OKOH4aH1-10 -en s Partizip II. singen - sang - gesungen finden - fand - gefunden BcnoMoraTenbHble rnaronb1 B H0M04KOM R3blK0 TpH BCnOMOraT011bHblX maro11a: sein, haben, werden, c11y)l(a1J.11-10 A11R 06pa3oeaH"1R CllO)l(HblX Q>opM. Cnpsi>1<eH1o1e ecnoMorarenbHblX rnaronoe: HacTosi114ee epeMR sein haben werden ich bin habe werde du bist hast wirst er, sie, es ist hat wird wir sind haben werden ihr seid habt werset sie, Sie sind haben werden npoWeAwee epeMR ich war hatte wurde du warst hattest wurdest er, sie, es war hatte wurde wir waren, hatten, wurden ihr wart hattet wurdet sie, Sie waren hatten wurden BpeMeHa rnarona HacToR114ee epeMR (Praesenz) 06o3Ha4a0T A0iiiCTBH0 np1-1eb14H00, nocrn- RHH00 "111"1 npOHCXOARIJ.100 B AaHHbliii MO- M0HT. 06pa3y0TCR np1-16ae110HH0M 11H4Hb1X OKOH4aHHiii K OCHOB0 maro11a: ich tanze wir tanzen du tanzt ihr tanzt er, sie, es tanzt sie, Sie tanzen npocToe npoWBAWH (lmperfekt) YnoTpe611ReTCR B OCHOBHOM B nHCbM0HHoM pe4H HllH B nOC110AOBaT0llbHOM noeecTBOBa- HHH AflR 00o3H840HHR AeMCTBHM, npoMCXO- AMBWMX B npowJIOM. rloKa3aT011b lmperfek.t y c11a6blx r.narollOB - ~c te- . CT~ OCHOBOiil Iii OKOtf'latMBll y CMl1bHblX - YepeAOBaHHe KOpHeeoro macHoro. ich sagte, sang du sagtest sangst er, sie, es sagte, sang gen wir sagten, sangen ihr sagtet sanget sie, Sie sagten, san- npoweAwee coeepweHHoe (Perfekt) 06o3Ha4aeT AeiiicTBH0, coeepw0HH00 B npOWllOM. 06pa3y0TCR c noMOLJ.blO BCnOMO- raT011bHOro maro11a haben e 11H4HOiii Q>opMe HaCTOR1J.1ero epeMeHH + Partizip II CMb1c110- eoro maro11a. ich habe gesagt du hast gesagt wir haben gesagt ihr habt gesagt er, sie, es hat gesagt sie, Sie haben gesagt 8HMM8HMe! c maro11aM"1, 0603Ha4alOIJ.1"1M"1 AB"1)1(0H"10 HllH H3M0H0HH0 COCTORHHR B Perfekt ynoTpe611ReTCR enoMoraTe11bHb1iii maro11 sein. ich bin geflogen du bist geflogen wir sind geflogen ihr seid geflogen er, sie, es ist geflogen sie, Sie sind geflogen nmocKeaMnep<t>eKT (Plusquamperfekt) 3TO ep0MR o6o3Ha4a0T A0iiiCTBHR, 3ae0p- W0HHbl0 B npOWllOM "111"1 np0AW0CTBOBaB- WH0 APYrHM A0iiiCTBHRM e npow110M. 06pa- 3y0TCR c nOMOLJ.blO BCnOMOraT011bHOro ma- ro11a haben (AllR maro11os, o6o3Ha4al0Ll.HX ABHll<0HH0 .,, "13M0H0HH0 COCTORHHR - sein) B 11"14HOiii Q>opMe npoweAwero ep0M0HH nlllOC Partizip II CMb1c11oeoro maro11a. ich hatte gesagt wir hatten gesagt du hattest gesagt ihr hattet gesagt er, sie, es hatte gesagt sie, Sie hatten gesagt ich war geflogen wir waren geflogen du warst geflogen ihr wart geflogen er, sie, es war geflogen sie, Sie waren geflo- gen 6y,qy114ee epeMR (Futurum I) 0603Ha4a0T A0iiiCTBH0, KOTOp00 np0"130iii- A0T e 6YAYIJ.10M. 06pa3y0TCR c noMOLJ.blO ecnoMoraT011bHoro maro11a werden e 11"14- Hoiii Q>opMe + MHcj>MHMTMB CMblCllOBOro ma- ro11a ich werde gehen du wirst gehen er, sie, es wird gehen gehen wir werden gehen ihr werdet gehen sie, Sie werden 6YAYL14ee e npoweAWeM 06o3Ha4a0T A0iiicTe1o10, KOTopo0 3ae0pwHT- CR B 6YAYLJ.0M, 111-160 np0An0110)1(HT011bH00 A0iiiCTBH0 e npow110M. 06pa3y0TCR c noMo- LJ.blO ecnoMoraT011bHOro maro11a werden e 11"14Hoiii Q>opMe + Partizip II CMb1c11oeoro maro11a + MHcj>MHMTMB ecnoMoraTenbHoro rnarona haben (Sein). ich werde geschrieben haben du wirst geschrieben haben er, sie, es wird geschrieben haben wir werden geschrieben haben ihr werdet geschrieben haben sie, Sie werden geschrieben haben 11HtPOPMB4MOHHO-cnpaa04HBR ra6nM4a N r- © 0 00 •l1HtPonnacr ", 2003 119180 r. MOCKBB, yn. 6. nonRHKa, ll· 24, ren.: (095) 230- 0608109, tPBKc; (095) 230-7111 N 0 .,., 0 0 0 r- 0 0 1D
www.infoplast.ru Cnoeapb noeceAHeeHoro o6~eHMSI -------.....0Ae>KAa Die Kleidung CKOllbKO CTOl1T ..? KaKoM y sac pa3Mep? 6e11be 60COHO>KKl1 60Tl1HK11 6t0CTrallbTep raflCTYK AeweebtM A>K11HCbl AOporoM, -afl 30HT wanKa KO>Ka KOllfOTKl1 KOCTIOM KOWeneK Kpy>KeBO KynallbH11K KYPTKa HOCKl1 HOYHafl py6awKa nanbTO nepYaTK11 n11>KaMa nnaTbe n11aU1- AO>KAeB11K nOflC pa3Mep py6awKa pyKaB CBl1Tep CYMKa TycjJ1111 QJYT6011Ka wapcjJ we11K wepCTb w11flna wopTbl I06Ka Wieviel kostet. ..? Welche Groesse haben Sie? die Waesche die Sandaletten die Halbstiefel der Buestenhalter die Kravatte bi/lig die Jeans teuer der Regenschirm die Muetze Leder die Strumpfhose der Anzug (My>KcKoii); das Kostuem (>KeHcK11ii) die Geldboerse die Spitze der Badeanzug dieJacke die Socken das Nachthemd der Mantel die Handschuhe der Sch/afanzug das Kleid der Regenmantel der Gurt (Gurtelj die Groesse das Hemd der Aermel der Pullover die Tasche die Schuhe das T-shirt das Halstuch die Seide die Wolle derHut die Shorts der Rock '-'eern Die Farben 6e>KeBbtM beige 6e11btM weiss >KellTblM gelb 3e11eHbtM gruen KOp11YHeBblM braun KpaCHblM rot opaH>KeBblM orange p030BblM rose CBeTllblM hell cepbtM grau Cl1Hl1M blau TeMHblM dunkel QJ110110TOBblM violet!; Ii/a ciepHblM schwarz AeHbrH, 6aHK, noKynKH Das Geld. Der Bank. Kaufen CKOllbKO 3TO CT011T? 5'I 6bl XOTell... no>Ka1iyMcTa 3To AOporo! nOAaBaTb >Kano6y o6Halll1'-111Tb YeK 3aKa3aTb on11aTl1Tb CYeT 6anaHc Wieviel kostet es? /ch moechte... bitte Das ist teuer! sich beschweren einen Scheck einlosen bestellen die Rechnung begleichen die B lanz 6aHKOBCK11M CYeT das Konto AaTa nnaTe>Ka der Zahlungstermin AeHbrl1 das Geld AOCTaBKa die Lieferung Kacca die Kasse Kacc11p (a 6aHKe) der Kassier KOMaHA11POBKa die Dienstreise KpeAl1TKa die Kreditkarte Kypc (BMIOTbl) der Wechselkurs MellO'-lb das Kleingeld HM11'-1Hble das Barge/d Hanor Steuer 0611araTb HanoroM besteuern o6MeHHblM nyHKT Wechselstelle onnaTa die Bezahlung OTAen npOAa>K die Verkaufsabteilung nepeBOA11Tb AeHbrn das Geld ueberweisen nl1CbMeHHO schriftlich noKynaTellb der Kaeufer npOAaBaTb verkaufen np0Aaee4 der Verkaeufer npo4eHT dieZinsen pacnpOAa>Ka der Ausverkauf paCXOAbl die Ausgaben; die Kosten peK11aMa411fl die Reclamation c6epe>KeH11fl die Ersparnisse ccieT (3a noKynKy, die Rechnung ycnyry) TaMO>KHfl dasZollamt TOproBllfl der Handel TpaTbl die Ausgaben yH11eepMar der Kaufhof yc110011flAOCTa0K11 Lieferungsbedingugen yc110011fl on11aTb1 Bezahlungsbedingungen 4eHa der Preis 4eHHOCTb der Wert 3KOHOMl1Tb (AeHbf11) das Geld sparen 3Aopoebe Die Gesundheit aHTl16110Tl1K aHrnHa aHTl1CenTl1K anTeKa 6011e3Hb 6011b e ropne 60llb 6pOHXl1T spay rnnc rp~yCH11K rp11nn A11arH03 3y6Hafl 60llb l1HQJeK4l1fl Kan1111 Kawenb KpOBb neKapCTBO Ma3b M11KCTypa (OT KaWllfl) HeceapeH11e>Ke11yAKa O>KOr onyxw11M na411eHT npOCTYAa COllHe'-IHblM O>KOr cpeACTBO TBMnepaTypa (BblCOKafl) TOWHOTa TpaBS'lHOM YaM YKOll das Antibiotikum dieAngine Antiseptikum die Apotheke die Krankheit Halsschmerzen derSchmerz die Bronchitis der Arzt das Pf/aster das Thermometer die Grippe die Diagnose Zahnschmerzen die lntektion die Tropfen der Husten das Blut die Arznei die Sa/be die Hustenmixtur Verdauungsstorung die Brandwunde geschwollen der Kranke die Erkaeltung das Rezept die Sonnenbrandwunde das Hei/mittel der Fieber die Uebelkeit der Kraeutertee die lnjektion 48CTb 2 YYe6a, pa6oTa Das Studium, die Arbeit YYl1T0Cb! Pa6oTaMTe! YYl1TbCfl a ey3e no cne411anbHOCT11... Studieren Sie! Arbeiten Sie! (ein Fach) studieren 3apa6aTbtBaTb AeHbrn Geld verdienen npoXOA11Tb Kypc (no...) einen Kursus durchmachen 6yxranTep der Buchhalter 6yxramepcK11M yYeT die Buchfuehrung peK11aMa die Reklame ryMaH11TapHbte HayK11 die Geisteswissenschaften KH11ra KHl1>KHblM Mara311H 6113Hec-06yYeH11e KaMnyc Kapbepa KOnnera KOllfleA>K 11HQJOpMaTl1Ka Kypc cTeneHb cnoeapb 06pa300aH11e 3H411KllOneA11fl 3K3aMeH cj:Ja6p11Ka 11306pa311T01lbHOe 11CKYCCTBO das Buch die Buchhandlung Ausbildung in Kommerz DerKampus die Kariere; die Laufbahn der Kollege; die Kollegin Der College die lnformatik derKursus der (akademische) Grad das Woerterbuch die Bi/dung die Enzyklopaedie die lmmatrikulation die Pruefung die Fabrik der bildende Kunst 11HocTpaHHb1e fl3blK11 die Fremdsprachen AHBBHOe (OTABfleH11e, das Direktstudium 06yYeH11e) 04eHKa MeCTO pa60Tbl npaeo iop11A11YecK11M cjJaKyllbTBT 611611110T0Ka die Note dieArbeit dasJura die juristische Fakultaet die Bibliothek cne411a11113a411fl die Spezia/isierung ecTecrneHHbre HayK11 die Naturwissenschafte eeYepHee (OTAeneH11e, abend 06yYeH11e) npenoAaBaTenb AOKll~ pacn11caH11e WKOna 3aHS'lTl1fl pa6oTa no11Hafl 3aHS'lTOCTb YaCTl1'-1Hafl 3aHflTOCTb der Dozent, der Lektor Der Vortrag der Stundenplan die Schute dieStudien dieArbeit die Vollbeschaftigung die Tei/beschaftigung EAa, pecTOpaH Das Essen, das Restaurant 5'! 6b1 xoTen... /ch moechte... 5'I 6b1 xoTen 3aKa3aTb... /ch moechte bestellen... CYeT, no>KanyMcrn! Die Rechnung, bitte! 3a CTOllOM Am Tisch Bl111Ka der Gabel ropci114a der Senf >KapeHafl KapTOWKa die Bratkartoffeln 3aBTpaK der Fruehstueck 3aKyCKa die Vorspeise Maeno die Butter HO>K der Messer nepe4 der Pfeffer np11eM n11U111 die Speise pacT11TellbHOe Maeno das Oel cancjJeTKa die Serviette COllb das Salz cne41111 die Gewuerze CTaKaH das Glas Cb1p die Kaese
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MocKaa, Kaw11pcKoe wocce, 21 E-mait mail@infoplast ru Http:llwww.infoplast ru Ten.: (095) 320-94-89 Cl>aKc: (095) 320-94-88 d, 00 N 0
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3HaKM npenMH3HMSI npM npMnO>KeHMSIX 06oco6mnoTcR npMMepbl. 1 . OAlllHO'IHble 11111111 pacnpoCTpaHeHHble YroMneHHbti!t 11.onroi!t pe'lb/O, fl 3aKpbtn rna3a 11 3acHyn. Ho Tbt B3b11-pan, Heo11.on11Mbti!t, 11 cornacosaHHble np11111o:>KeH111R, ec11111 OTHOcsncR K 11111'1HOMY MeCTOlllM€HllllO. CTafl TOHeT KOpa6nei!t. 2. PacnpocTpaHeHHb1e cornacosaHHb1e np11111o:>KeH111R , KOTOpble CTORT noc11e onpeAe11ReMOro '-lacbt, npoao11.11Mbte c Mono11.e:>Kb10, 6btnl1 3apR.£J.KOi!t 6011.pocm Anfl naana. cy~eCTBlllT€11bHOro 3. OAlllHO'IHble cornacosaHHb1e np11111o:>KeH111R, ec11111 CTORT noc11e onpeAe11ReMoro cy~.• ec11111111x 6011bwe Tearp oca>K,llano Mono11.oe Mope, 6yi!tHoe, Hanop11croe. ConHue, aen11KonenHoe 11 OAHOro , B oco6eHHOCT111 ec11111 nepeA cy~. y:>Ke ecTb flPKOe, nO,[J,Hl1Manocb HB,ll MOpeM. onpeAe11eH111e. 4. CornacosaHHoe np11111o:>KeH111e, CTOR~ee snepeA111 onpeAe11ReMoro cy~ecTB111Te11bHOro , c A06aso'IHblM np11Bne'leHHble RPK11M CBeTOM, 6a60'IKl1 np11neTen11 11 Kp}'>Kl1nl1Cb OKOnO </>OHBpfl. o6CTORTe11bCTBeHHblM 3Ha'leHll1€M . BBOAHble C110Ba Ill KOHCTPYKU,111111 Bb1Ae11RIOTCR 3anRTOi:1: KoHe'IHO, He O,QHH EsreHHH CMJITeH&e TaHH BH,QeT& MOr. 81>1, JI BHJKY, nio6HTe npHpO,Qy. He RB11RIOTCR BBOAHblMlll Ill He OTAe11RIOTCR 3anRTblMll1 C110Ba Ill C110BOCO'leTaH111R: BBOC&, 6yKsan&HO, 6y.QTO, s.qo6asoK, B,QOBepweHHe, s.qpyr, B KOHe'IHOM C'leTe, BPJIA nH, sce-TBKH, e,QBB nH, KBK 6y.QTO, KBK 61>1, K TOMY JKe, MeJKAy TeM, no peweHHIO, npH6nH3HTen&HO HAP· 06oco611RIOTCR npMMepbl 1 . ,[J,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1 11111111 HeCK011bKO Aeenp111'1aCTll1i:1 , OTHOCR~lllXCR K OAHOMY ConHue. cnpRraaw11cb 3a y3Koe c113oe o6naKo, 3onornr KpaR ero. rnaro11y. 2 . OA111HO'IHb1e Aeenp1114acrnR (He B 3Ha'leH111111 nowyMeB, peKa ycn0Ko11nacb, BHOBb nerna a 6epera. Hape'l111R). He 06oco611R10TCR npMMepb1 ' 1 . ,lJ,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1, npesparnsw111ecR B ycTOi:1'1111Bb1e o6opoTbl pe'l111 : cnycrn pyKasa,c110MR ro11osy, He nepeBOAR Ab1xaH111R Manb'll1K 6e>Kan cnoMR ronoay {o'leHb 6btCTpo). lllAP· 2 . OAlllHO'IHble Aeenp1114acT111R, 111Me10~111e 3Ha'leH111e flKOB wen He TOpOnflCb (Me,[lneHHO). 0 nporynKe OH paCCKB3btBan CMeflCb (Becena). Hape'l111R. 3. ,lJ,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1 , TeCHO no CMblC11Y C11111Bal0~111eCR c rnaro110M . Crap11K c1111.en onycrna ronoay. 4 . rpynnbl OAHOPOAHblX '111eHOB, COCTOR~llle 1113 Manb'l11K OTBe'lan OTKPOBeHHO 11 H11CKOnbKO He CMyll.jaf/Cb. Hape'llllR 111 Aeenp111'laCrnR . npM OTCYTCTBMM marona - CBR3KM CTBBMTCR TMpe 1 . Ec11111noAne:>Ka~ee111 CKa3yeMoe - cy~ecTB111Te11bHb1e B VIM. n. 2 . noAne:>Ka~ee Ill CKa3yeMOe Bblpa:>KeHbl '1111C11111Te11bHblMll1 B VIM. 11111111 OAlllH 1113 HlllX - '1111C11111Te11bHOe, BTOpoi:1 - cy~eCTBll1Te11bHOe B VIM.n. KH11ra - 11cTO'IH11K 3HaH11i!t. nf/Tb/O BOC8Mb - COPOK. ,[ln11Ha 80nrl1 - 3688 Kl1nOMeTpOB. >K11Tb - po11.11He cn}'>Kl1Tb. 4 .0AlllH 1113 rnaBHblX 'IJleHOB npeAflO:>KeHlllR Bblpa:>KeH lllH<)>lllHlllTlllBOM, a Apyroi:1 - cy~ecTBlllTenbHblM B VIM . n . np0113BO,[J,11Tb 3<f><f>eKT - 11X Hacna>K,[leHl18. T111pe He CTaBlllTCR, ec11111 nepeA CKa3yeMblM CTOlllT OTp111u,aH111e HE 11111111 cpaBHlllTeJlbHble COI03bl : KBK, TO'tHO, KBK 6yATO M AP·: npy.Q KBK 6neCTJIU(ee 3epKano. Cep.Q14e He KBMeH&. Ec11111 nOAfle:>Ka~lllM RBJlReTCR 11111'1HOe MeCTOl11MeH111e, TO Tlllpe , KaK npas111110, He CTaBlllTCR: OH CKenTHKH MBTepHBnHCT. VICKJ1IO'l€Hllle: np111 nOA'lepKHYTOi:1 3Ha'lll1TeJ1 bHOCTll1 BblCKa3blBaHll151, ec11111 Ha M€CT0- 111M€Hllle 111 3Ha 'le H111e nC!MleT 11or111'lecKoe yAape H111e : OH - sawa PBAOCT&, sawa cnasa! Ec11111 n e pe.a CKB3ye MblM CTOIH CJ10Ba B OT, 3 --/Ji ITT 3TO TO rnpe CTaBITTCSI n EPEJJ. 3Tlll Ill : T041HOCTJ. If tcpaTJCOCTJ. - SOT nepswe AOCTO#HCTBB npo3b1. MH¢tOpMaLl.MOHHO- cnpaao'iH8A Ta6nM~ © 000 •lllH<l><>nnacT-, 2006 r. Moc<sa, KawMpc1<oe wocce. 21 E-mail mai@inloplasLru: Http/ c ...... c
06PA30BAHHE ~ 6GKMM A3blK 3HaKM npenMH8HMSI B cnO>KHOM npeA,nO>Ke MM. 3ansnasi He CTaBlllTCSI: 1. Me:>t<Ay npeAflOJKeHlMlMlll, coeA111HeHHb1M111 COYlllHlllTenbHblM 111n111 pa3Aen111TenbHblM COI03aMlll, ecn111 lllMelOT 0614111~ BTOpOCTeneHHbl~ YneH 111n111 0614ee np111AaTOYHOe npeAflOJKeH111e. 3ansiTaSI CTaBlllTCSI: 1. Me:>t<Ay npoCTblMlll npeAflOJKeH111siM111,sxoAS1l4lllM111 s COCTaB cnOJKHOCOYl!IHeHHOro. TO"IKa c 3anSITOM CTaBlllTCSI: 1. Ecn111 coeA111HsieMb1e npeAflOJKeH111si 3HaY111TenbHO pacnpocTpaHeHbl, 111Me10T BHYTPlll ce6si 3anS1Tb1e 111n111 MeHeeTeCHO cssi3aHb1 Me:>KAY co6o~ no CMb1cny. T111pe cTae111Tcsi: 1. Bo BTOPOM npeAflOlKeHllllll COAeplKlllTCSI HeOJKlllAaHHoe np111coeA111HeH111e 111n111 pe3Koe npoT111sonocTasneH111e. 0TAensieTcsi 3ansiToit: 1. np111AaTOYHOe npeAflOlKeH111e OT rnaBHOro. Ecn111 OHO CTOlllT BHYTPlll rnaBHOro, TO c ABYX CTOPOH. 2. np111AaTOYHble npeAflOlKeHlllSI C COCTaBHblMlll COI03aMlll nOTOMY 'ITO, BMeCTO Toro 'IT06bl, nocne Toro KaK 111 AP· (np111YeM 3ansiTasi cTaBlllTCSI n11160 nepeA BCeM COCTaBHblM COI030M, n11160 nepeA 'ITO, 'IT06bl1 KaK, B 3aBlllClllMOCTlll OT lllHTOHau,111111 Ill CMblCna). 3anSITOM He OTAensieTCSI: 1. HenonHoe np111AaTOYHoe npeAflOJKeH111e, cocTosi14ee 1113 OAHOro cnosa 111n111 co103a. He pa3AensiioTcsi 3ansiTb1M111: 1. Hepa3nOlKlllMble COYeTaHlllSI: CAenaTb KBK cne,qyeT, CAenaTb KaK nonano, npHXOAHT& KOrAa B3AYMBeTCR, HATH KYAB rna3a rnRART, KpH'l8Tb 'ITO eCTb MO'IH, 6yA& 'ITO 6yAeT Ill AP· 2. CoYeTaHlllH He TOn&KO 'ITO, He TO 'ITO, He HHB'le KaK, TOn&KO 'ITO He, see paBHO 'ITO Ill AP· 1. 06opOTbl , HaY111Ha1014111ecS1 cpaBHlllTenbHblMlll COI03aMlll KBK, 6yATO, cnOBHO, TO'IHO, 'leM, HeJKenH, KBK 6yATO Ill AP· 2. 06opOTbl , HaYlllHa1014111ecsi COYeTaHlllSIMlll KBK ff, KBK npaBHnO, KBK HC/Ul/O'leHHe, KBK scer1ta, KBK HapO'IHO Ill AP-. KPOMe Tex, YTO BXOASIT B COCTaB cKa3yeMoro. np111Mepb1. V13 oKowKa )J,aneKo 6necrnT ropbt 11 BM)J,eH /J,Henp. np111Mepb1. 803)1,YX )J,b/WMT aeceHHMM apoMaTOM "1 BCR np11po)J,a O>KMBflReTCR. np111Mepb1. TaTbRHa, no COBeTY HRHM co611paRCb HO'lb/O BOPO>KMTb, TMXOHbKO npMKa3ana B 6aHe Ha )J,Ba np116opa CTOfl HaKpblTb," HO crnno CTpawHO BAPY• TaTbRHe. np111Mepb1. OH 3HaK no)J,aCT - "1 Bee XOX04YT. np111Mepb1. Kor)J,a COflHl..je nO)J,HMMaeTCR Ha)J, nyraMM, R HeBOflbHO ynb16at0Cb OT pa)J,OCTM. Ha)J, )J,OflMHoilr, r)J,e Mbt exan11, cnycTMflMCb TY4M. - OH He RBMflCR Ha 3aHRTMR, noTOMY 4TO 3a6onen. He XO)J,"1 B arnKy )J,0 TeX nap, noKa He nony4MWb OT MeHR npMKa3a. np111Mepb1. MeHR cnpoc11n11, Ky)J,a R noe)J,y neTOM. fl o6bRCHMn Ky)J,a. np111Mepb1. OH BbtnOflHMn pa6oTY KaK cne)J,yeT. OH np11xo)J,11n KOr,ll,a B3,ll,yMaeTCR 11 yxo)J,11n He npo~aRcb. CecTpa 6b1na MHe ace paBHO 4TO MaTb. 111 neHl!IBO, KaK 6bl 3acb1naH, YAap111n OAlllH pa3 B KOnOTYWKY HOYHO~ CTOPOlK. Bo~Ha 3anOMH111nacb MHe 6onbwe pa6oTo~. YeM yYe6o~. KaK npas111no, s 3Tl!IX Mecrnx 6b1sa10T 06111nbHb1e AO:>t<Alll (cp.:B 3Tlllx MecTax 06111nbHb1e AO:>t<Alll 6b1Ba10T KBK npaBHno ).
1. Ecm-1 o6opoT 1'1MeeT 3Ha4eH1-1e 06cTosne11bcTsa 06pa3a Aei1crn1-1si (11erKo 3aMeHl'1Tb TponffHKa ff3Bffaanacb KaK 3MeR (3Meei'I). Hape41-1eM 1-1111-1 cpopMoi1 Tsop.n .cy11.1.) . 2. np1-1 3Ha4eHl'11'1 OTO)l(AeCTB11eHl'1SI. 0Ha cMoTpena Ha MaTb KaK Ha crapwy10 cecTpy. 3. np1-1 nepeAa4e 3Ha4eHl'1SI "s Ka4eCrne". OH cen 3a pynb KaK wocf;ep. 4. Ec111-1 SIBllSleTCSI CKa3yeMblM 1'1111'1 TeCHO K HeMy npL'1MblKaeT. >K1113Hb KaK nereH,IJ,a. Ha 3KpaHe ace 6b1no KaK a >Klll3Hlll. 5. EC111'1 eCTb OTpl'1L(aHl'1e He 1'1111'1 CllOBa cosepweHHO, nO'ITJ1, spo1te 'TO'lb-B·TO'lb, OH ace ,1J,enaeT He KaK n10,1J,111. Ho'lb/O a ropo,IJ,e 6blflO 1o1MeHHO L'1 AP- caemo no•-1T111 KaK .D.HeM. 6. Ec11L'1 3TO ycToi141'1BOe Bb1pa:>KeHL'1e: 6ne1tH&1if KaK CMepr&, 6necrer& KaK OH 3awen KO MHe 6ne,/],Hb/M KaK CMepTb /II 3epKano, rono1tH&1if KaK co6aKa, seprer&c11 KaK 6enKa s Konece L'1 AP· . MOfl'lafl/llBbliii. 3HaKLll npenLllH3HLllSI B 6eccol03HOM CJlO>KHOM npeAJlO>KeHMH.r~~.~•• 3anRT8SI CT8Bl'ITCSI: np111Mepb1. 1. EC111'1 npeAJ10:>KeHL'1SI o603Ha4atoT OAHOBpeMeHHO 1-1111-1 noc11eAOBaTellbHO Me:>KAy co6oi1, Kparrn . .llaneKO 3a .lloHOM rpOM03,IJ,/llfl/llCb TR>Keflb/e TY'llll, pe3an111 He6o MOflH/11/11, 'IYTb Cflb/WHO rpOMb1xan rpoM. TO'"IK8 c 3anRTOH CT8BMTCSI: 1. EC111'1 npeAJ10:>KeHL'1SI MeHee CBSl3aHbl no CMblCllY L'1 6011ee pacnpocTpaHeHbl (oco6eHHO ec11L'1 BHyrp1-1 HL'1X eCTb 3anS1Tble). BpeMR CTO/llT e~e paHHee, wecmiii 'lac B Ha'lane; 30JlOT/llCTbliii yrpeHHllliii TYM8H BbeTCfl Ha,IJ, npocenKOM, e,1J,Ba nponycKaR TOflbKO 'ITO noKa3aaweecR conH4e; Tpaaa 6necT111T. AeoeTO'"IMe CTae111Tcsi: np111Mepb1. 1. Ec111'1 BTopoe npeAJ10:>KeHL'1e AOno11H51eT nepsoe. Haaepxy>Kypaan111Hb1iii Kp111K: nT1114b1 ynera10T Ha 10r. 2. Ec111'1 BTopoe npeAJ10:>KeHL'1e pacKpb1saeT coAep:>KaHL'1e nepsoro, nosicHsieT ero 1'1111'1 KaKOi1-Hl'16YAb ero 411eH. Cmnb aeceno necTpeeT 4aeTaMw RpKo >KenmeT.D.POK, CKPOMHO ClllHelOT KOflOKOflb'l/llK/11, 6eneeT 4enb/M/ll 3apocnRM/ll naxy'laR poMawKa. 3. Ec111-1 BTopoe npeAJ10:>KeH1-1e yKa3blsaeT npi-t4"1HY Toro, o 4eM rosop1'1TCSI s nepsoM. 8,!J,pyr fl 'IYBCTBylO: KTO-TO 6epeT MeHR 38 nne'le /II TOnKaeT. I J~-~~r~ -i.-ir-~=·- . - • :_ II.- f"."!:• TL11pe Me>K,ly noA11e>KaW.L11M Lil cKa3yeMblM.~.. T111pe cTae111Tcsi: np111Mepb1. 1. EC111'1 npeAJ10:>KeHl'1SI pl'1CYIOT 6blCTpyto CMeHy co6b1rni1 "111"1 npocHyncR - nRTb CTaH4/llM y6e>Kano H83a,IJ,. Cblp BbJnan - c H/llM 6blfl8 HeO:>K1'1AaHHbli1 pe3yllbTaT Aei1CTB"1SI. nnyrOBKa TaKOBa. 2. Ec11i-t B npeAJ10:>KeHL'1SIX COAep:>Ki-tTCSI npornsonocTas11eHi-te. Bab/Cb a3neraeT CoKon - >KMeTCR Y>K K3eMne. 3. Ec11i-t nepsoe o6o3Ha4aeT speMsi i-t11i-t yc11osl'1e Aei1cTBl'1SI, o f1ec py6RT - ~enK/11 nernT. Ha3aancR rpy3,IJ,eM none3ai'I a KY30B. KOTOPOM rosopl'1TCSI BO BTOPOM. 4. EC111'1 TO, 0 4eM rosopl'1TCSI B nepBOM npeAJ10:>KeH"11'1, cpaBH"1BaeTCSI Mona111T cnoao - conoaei'I noeT. c TeM, 4TO CKa3aHo s APYrOM . 5. Bropoe npeAJlO:>KeHi-te 3aKJlto4aeT s ce6e pe3y11brar Aei1crni-tsi s ConH4e .D.blMHoe acraeT - 6y,1J,eT ,1J,eHb ropR'lllliii. nepBOM, BblBOA "13 Hero. 1. Ecn111 cnoea aeTopa CTOSIT nepeA npsiMOH pe'"lblO: 1. To noc11e HL'1X CTaBL'1TCSI ABOeT04"1e. BanR, Tenno o6HRB 3a nne'l/11 MaTb, ycn0Ka111aana ee:''Tbl He TpeBO>KbCR, MaMa ". 2. Ecn111 npsiMasi pe'"lb CTOMT nepeA cnoeaM111 aeTopa: 1. To noc11e Hee CTaBi-tTCSI 3ansiTasi .,, T1-1pe. "fl m6R H/llKOMY He BbJ,IJ,aM",- mp>KecrneHHO o6e~ana OnR. 2. EC11"1 B npSIMOi1 pe4"1 COAeP:>K"1TCSI sonpoc "111"1 BOCKJ1"1L(aHi-te, TO nocne CTaBi-tTCSI sonpOC"1TeflbHbli1 "1Jl"1 BOCKJ11'1L(aTeflbHbli1 3HaK.,, Ti-tpe. "KTO 3TO 6bln?" -He,IJ,OyMeHHO no,IJ,yMan OH. 3. Ecn111 cnoea aeTopa H8XOARTCR e cepeAMHe npsiMOH pe'-1111: 3.a) EC11"1 Ha Mecre pa3pb1Ba AOll)l(Hbl 6blJ1"1 CTOS!Tb He T04Ka, sonpOC"1TeflbHbli1 3HaK "111"1 BOCKJ11'1L(8TeflbHbli13HaK"1, TO CJlOBa aBTOpa Bb1AellSllOTCSI c o6ei-tx CTOpOH 3anS1TblM"1.,, rnpe. "fl saw OP/J.lllHaTOp - cero,1J,HR ,1J,e>Kyp10". 3.6) EC11"1 Ha MeCTe pa3pb1Ba AOJl:>KHa 6blfla CTOS!Tb T04Ka, TO nepeA CllOBaM"1 aBTOpa CTaBL'1TCSI 3ansiTasi .,, rnpe, a nocne - T04Ka L'1 rnpe. Brnpasi 4aCTb npsiMoi1 pe4i-t - c 6011bwoi1 6yKBbl. 'Taoe nplllCYTCTB/lle 3,IJ,eCb Heo6XO,IJ,/llMO, - CKa3ana OHa. - np111e3>Kaiii". 3.B) EC11"1 Ha MeCTe pa3pb1BaAOfl:>KeH CTOS!Tb sonpOC"1TellbHbli1 "111"1BOCKJ11'1L(8TeJ1bHbli13HaK, TO nepeA CllOBaMi-t asrnpa CTaBi-tTCSI 3TOT 3HaK.,, rnpe, a noc11e • T04Ka L'1 rnpe. Brnpasi 4aCTb npSIMOi1 pe41'1 - C 6ollbWOi1 6yKBbl. ''no'leMy BBOCeMb?- cnpoc111na OHa. - Mara3/11Hbl 38Kpb!B810TCR KweCT/11". l/IH<jlOpM34110HHO· cnpaeO'lHa11 rn6n1143 © 000 « lllHcponnacr", 2007 r. r. MOCKBa, Kaw~pcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru
OliPA30BAHHE CnMCOK HeK0Topb1x Hape'"IMM M H Bblpa>KeHMM. B6nll131!1 BneperoHKl!l 6e3 B8AOMa 6e3 cnpocy B60K BnepeMe:>KKY 6e3 Orn5lAKl!1 6e3 TOnKy no ABOe B6pOA (OT 6e3 OTKa3a 6e3 YMOnKy nOA KOHeu,nepeMe>KaTbCR) BB8K 6e3 npocBern 6e3 ycrnn111 nOA MblWKaMl!lBnepeMeWKY 6e3 pa36opy 6oK o 6oKBBepx (OT nOA Mb1WKl!1 BBblCb nepeMew111BaTb) (B3f1Tb) Brny6b Bnono6opoTa 3a rpaH111u,eVI 3aOAHO nOAP5lA BAaneKe BnOnOBl!IHY 3a rpaH111u,y 3anaH1116parn noA c111ny BAanl!1 Bnopy(no 3aMY:>K 3a nonHO'-lb nOA CTaTb BAanb MepKe) 3aMY:>K8M nOA Y3AU,bl BABOe B nopy (BO Ha aBOCbBpeMR) BA06aBOK Ha 6ery HanoKa3 C B8AOMaBnocneACTBl!11!1 BAOfOHKY BnOTbMaX HaBeK HanonOBl!1HY cBepxy AOHll13YBApe6e3rn HaB8Kl!1 (c,D.enaTb) BnpaBAY c MaxyB 3aKnl048Hl!18 HaBepx Ha nonnYT111 BnpaBe CMOnOAYB3aMeH Ha B3rn5lA HanononaM BnpoK c HaneryBKOH8LJ, HaB3Hl!14b Ha nopyKl!1 BnpocaK HanpoKaT CHl!13Y AOBepxyB KOHLJ,8 Ha Bl!IAB npOTl!1BOB8C KOHLJ,OB Ha Bl!1AY Hanpo4b Bpa3 B KOpHe Bpa36111BKY HaBp5lA n111 HapaBHe BKPYTYIO HaBCTpe4y HapacnawKy Bpa3pe3 BKyne HaBblT5l:>KKY Ha peAKOCTb BM1!1r Bpacnnox Ha pblC5lX AO KpaVIHOCTl!l BpaCCblnHylO Ha rna3 AOBHaV!Mbl Ha CKaKy BPOA8 Ha rna3oK Hey3HaBaeMOCTl!1 BHaKl!1AKY HaronoBy Ha cnaBy AOHl!13YBpyKOnawHyt0 B HaCM8WKY BP5lA n111 (pa36111Tb) HaCMepTb BHa'-lane Ha A111BO ( 611tTbCR) BHl/13 B cepAu.ax Ha AH5lX Ha CMepTb BCneA Ha Abl6bl (111,ll.Tlll)BHl!14bl0 B o6pe3 Bcnenyt0 Ha CMex Ha3aBTpa B o6w,eM Bcnyx HaCT8:>Kb Ha3no BOB8K B CTap1!1HY Ha3y6oK HayraA BOB8Kl!1 BCTapb HaKaHyHe HayAa'-ly BTaVIHe (CK838Tb) BOBP8M5l(B (xpaH11tTb) Ha neTy Ha XOAY HY:>KHblVI '-lac) BTP111AOpora Han1!1LJ,O Ha U,blnO'-IKax Bo Bceopy:>Kl!11!1 B XOAY Ha M111r Ha'-leKy B OAl!1H04KY B u,enoM Ha HeT Ha41!1CTOTY BO 1!136e:>KaHl!18 BW1!1pb Ha OTnl!14HO Ha5lBY BOl!1CTl!1HY B WYTKY HaOTMaWb H8B3Ha4aill Boo6w,e Bb5lBb Ha ow,ynb HenoAaneKy B OTKpblTYIO Hanepe6oill He noA c111ny BnepBble HaneperoHKl!1 He nOA CTaTb HanepeKop nOA'-laC nOA4111CTYIO no3aB4epa noHeBone nOOAl!1H04Ke no naM5lTl!1 no npaBy nocepeA111He no cTap111HKe nOYTPY cnne'-la (py611tTb) c pa3roHa c pa3Maxy CP5lAY CXOAY Cbl3HOBa 4epec4yp AO OTKa3a AO CBl!1AaHl!15l AOma
A6c~111cca anennS1~111S1 aKKI11t1MaT1113a~111S1 annapaT aKKOMnaHeMeHT annaCClllOHaTa aKKOMnaH111posaTb anneHA1t1~111T aKKOPA anneTlllT aKKYMYnSITOP annn111Ka~111S1 aKKypaTHblill apT111nnep111S1 annerop111S1 ac111MMeTp111S1 anneS1 accaM6neS1 ann111raTop ann111Tepa~111S1 anrnop aMMlllaK aHHOTa~lllSI aHHyn111posaTb aHT8HHa 6ann .(eA1t1H111~a 0~8HK111) 6annMa 6annacT 6annoH 6aJ1110WlpoBaTbC51 6apOKKO 6app111KaAa raMMa reHepan111cc111Myc rn66oH rnnnonoTaM aCCll1CT8HT accoHaHc accopT111MeHT acco~111a~111S1 anecTaT anpaK~1110H acpcpeKT 6acceil1H 6a~111nna 6enneTp111crnKa 6ecCOHHll1~a 6111cceKTp111ca 6occ 6p111nn111aHT HO: 6p1t1nbSIHT) 6t0nneTeHb BQ)t()f(l/1 B03)t()f(8HHblil1 Bbl)t()f(8HHbl111 rpaMM rpaMM8Tll1Ka rp111nn rpoccMeillcrnp rpynna rynanepYa A111Crnnn111posaHHb1!:1 All'l<PQ>epeH~anbHbl~ All'l<Pct>Y3111SI AOn11ap ,QpeCCll'lpoBaHHbli:1 111All'lnllll'ISI ll'IJ1Jll0311'1SI ll'IJlJllOMll'IHa~ll'ISI ll'IJlJllOCTpa~ll'ISI 111Mnpecc1110Hlll3M ll'IMMYHll'IT8T IllHAlll<l><i>epeHTHblH Ka11n111rpacp111S1 Kan111n11S1p Kacca Kacca~111S1 KacceTa K8CCOH KJ18CCll1~1113M KJ18MM8 Konnera Ko11ner11rn KOJ1n8KTll'IB KOJ1n8KTOp KOJ1J18K~ll1SI KOJlOHHa KOJlOCC (sen111KaH) KOMlllCCap KOMll1CCll1SI KOMM8HTap11111! Macca Macca)K M8CCll'IB MeTann Met.tt.to-conpaHo ceCCll'ISI cenep c111n11a6111yecK111il1 Cll'IMM8Tpll1SI ll'IHT8J1J18KT lllHTeJlJllllreHUlllSI 111nnOAPOM 111ppat.tlllOHaJlbHblH 111pp111ra~111S1 ll'ICKYCCTBO KOMMYHll13M KOMMYTaTop KOMMIOHll1K8 KOMnpecc KOMnpeccop KOMnpOMlllCC KOHrpecc KOH~8CCll1SI Kopann KOpp8KTHblil1 KOppeKTOp KOppecnOHA8HT KOpp03111SI Koppyn~111S1 KOTT8p)K K03cpcp111~1t18HT Kp111crnn11 Kp111craJ111w1ecK111H Kpocc KpOCCBOPA n1116peno MlllnJlll'IOH MlllCCll'ISI MO)t()f(888nbHll'IK MOnnlOCK MOHOrpaMMa MYCCOH Hose11na onno3111~111S1 onnoHeHT CT8J1Jla:>K CTpemOKOKK cy66orn na11a~~o naHHO napaJ111e11orpaMM napa11ne11b nacca)K nacca)K111p naccaT naccaT1t1)K1t1 naCClllBHblill Perpecc pe:>K111ccep TenerpaMMa T8HHll1C Teppaca Teppll'IKOH neppoH neCCll1Mll13M npecc npecca nporpaMMa nporpecc nponen11ep npocpecc111S1 Tpacca Tp11111n1t10H Tponneil16yc Tpynna ~ennt0no3a wocce sn111rpaMMa 3CC8H~ll1SI scpcpeKT © 000 «111Hcjlonnacr», 2008 r . MocKsa, Kaw1-1pcKOe wocce, 21 E-mail: mail@infoplast.ru Http://www.infoplast.ru Ten ./cjJaKc: (499) 940-93-23 Ill I4 607061 651873
06PA30BAHHE ~ PYGGKHH Sl3blK 0CHOBHble cxeMbl paa6opa B pycCKOM Sl3b1Ke. 1. CAenaTb TpaHcKp111rn..1,111io, nocTas111s YAapeH111e. 2. Pa36111Tb cnoso Ha cnorn. 3. OxapaKTep1113osaTb cnorn: a) YAapHbriil/ 6e3yAapHbriil; 6) 3aKpblTbliil/ OTKpblTbliil; 4. OnpeAen111Tb Kon1114ecrno 6yKB 111 3BYKOB, ycTaHOBlllTb COOTBeTCTBllle Me:>K,D,y HlllMlll . 5. OxapaKTep1113osaTb rnaCHb1e 111 cornacHbre 3syK111: a) rnacHbJiil : YAaPHOCTb/ 6e3yAaPHOCTb; 6) cornaCHbliil : rnyxoiil/ 3BOHK111ii1 ; rnepAbliil/ MS'lrKllliil. Mop<t>eMHblH paa6op. 1. Ha3BaTb 4aCTb pe4111 (1113MeHs:ieMas:i 111n111 Helll3MeHs:ieMas:i). 2. 8b1Aen111Tb OKOH4aH111e Ill OCHOBy. 3. noA60pOM POACTBeHHblX cnos BblAenlllTb KOpeHb cnosa. 4. noA60pOM cnos c OAlllHaKOBOiil CTpyKTypoiil BblAenlllTb np111crnsKy 111 cy¢¢111Kc. YcTaHOBlllTb 111x ¢YHKL.J,llllll B cnose. 5. lpa¢1114ecK111 BblAen111Tb see MopcpeMbl s cnose 111 CAenaTb BblBOA 0 ero COCTaBe. Mop<1>onon·1'~ecKl1H pa36op. rnarona. 1. Ha4anbHas:i ¢opMa (111H¢111H111rns) . 2. nocTos:iHHbre np1113HaK111: a) BlllA (cosepweHHbriil 111n111 HecosepweHHbriil); 6) B03BpaTHOCTb; B) nepeXOAHOCTb; r) rnn cnps:i>KeH111s:1. 3. HenocTOs:!HHble np1113HaK111: a) HaKnoHeH111e; 6) 4111cno; s) speMs:i (ecn111 ecTb) ; r) n111L.J,o (ecn111 ecTb); A) POA (ecn111 eCTb) . 4. cDyHKL.J,llls:l B npeMO>KeHllllll. npM'laCTJ1R. 1. Ha4anbHas:i ¢opMa (111MeH111T. naA. eA. 4111cna My>K. poAa) . 2. nocTos:iHHbre np1113HaK111: a) BlllA; 6) 3anor (AeiilcTBlllTenbHbliil 111n111 cTpaAaTenbHbriil); s) speMs:i. 3. HenocTos:iHHbre np1113HaK111 : a) nonHoe 111n111 KpaTKoe; 6) POA; s) 4111cno; r) naAe>K. 4.cDyHKL.J,llls:l B npeMO>KeHllllll. P,eenpM'laCTMR. 1. Ha4anbHas:i ¢opMa (111H¢111H111T111B rnarona) . 2. BlllA. 3. cDyHKL.J,llls:l B npeMO>KeHllllll. Hape'IMR. 1. Pa3ps:1A no 3Ha4eH11110. 2. CrnneHb cpasHeH111s:1 (ecn111 ecTb) . 3. cDyHKL.J,llls:l B npeMO>KeHllllll. Cnoeoo6pa3oeaTenbHblH pa36op. 1. YCTaHOBlllTb npOlll3BOAs:!W,YIO OCHOBY, 2. 8b1Aen111Tb cnosoo6pa3osarnnbHb1e a¢¢111Kcb1. 3. Ha3BaTb cnoco6 06pa3osaH111s:1 AaHHOro cnosa. YKa3aTb npoL.J,eccbr, conposo:>K,D,aiow,111e cnosoo6pa3osaH111e. Mop<1>onorw~ecKl1H paa6op. HMeHM cyu.iecTBMTen&Horo. 1. Ha4anbHas:i ¢opMa: 111MeH. naAe)J( eA. 4111cna. 2. nocTos:iHHbre np1113HaK111 : 1. Co6crneHHoe 111n111 HaP.1111.J,aTenbHoe. 2. 0AywesneHHoe 111n111 HeoAywesneHHOe. 3. KoHKpeTHOe,oTsne4eHHOe, co6111paTenbHOe, sew,eCTBeHHOe. 4. PoA: My>KcKoii1, >KeHcK111ii1, cpeAH111ii1. 5. T111n CKnOHeH111s:1. 3. HenocTos:iHHbre np1113HaK111: a) 4111cno; 6) naAe>K. 4. cDyHL.J,llls:! B npeMO)J(eHllllll . HMeHM npMnaraTen&Horo. 1. Ha4anbHas:i ¢opMa ( 111MeH. naA. eA.4. MY>K. poAa). 2. nocTos:iHHbre np1113HaK111: a) pa3ps:1A no 3Ha4eH11110 (Ka4ecrneHHoe, OTHOClllTenbHOe, nplllTs:l>KaTenbHOe); 6) y Ka4eCTBeHHbrx: nonHas:i 111n111 KpaTKas:i ¢opMa; B) y Ka4eCTBeHHblX: CTeneHb cpasHeHllls:l (nono)J(111TenbHas:1, cpasH111TenbHas:1, npesocxOAHas:i). 3. HenocTOs:!HHbre np1113HaK111: a) POA; 6) 4111cno; s) naAe>K. 4. cDyHKL.J,llls:l B npeMO>KeHllllll. HMeHM 'IMCnMTen&Horo. 1. Ha4anbHas:i ¢opMa (111MeH. naA.). 2. nocTOs:!HHble npi113HaKlll : a) neKClllKO-rpaMMaT1114eCKlllii1 pa3ps:!A (Kon1114ecrneHHoe, nops:iAKosoe, co6111parnnbHoe, AP06Hoe); 6) no CTpyKType (npocTOe, cnO>KHOe, COCTaBHOe); B) oco6eHHOCTlll CKnOHeHllls:l. 3. HenocTOs:!HHbre np1113HaK111: a) naAe>K; 6) POA (ecn111 eCTb); s) 4111cno (ecn111 ecTb). 4. cDyHKL.J,llls:l B npeMO>KeHllllll. MecTOMMeHMR. 1. Ha4anbHas:i ¢opMa (111MeH. naA. eA. 4111cna) . 2. nocTOs:IHHble npi113HaKlll: a) pa3ps:!A no 3Ha4eH111io; 6) oco6eHHOCTlll CKnOHeHllls:l. 3. HenocTos:iHHble np1113HaK111: a) naAe>K; 6) 4111cno (ecn111 ecTb); s) POA (ecn111 ecTb).
CnYJKe6HblX 'lacTeil pe'IM. 'lacnw,&1. 1. paaps:iA no 3HaYeH11110. npe1tJ10ra. 1. Henpo111aBOAHb1"111111111 npo1113BOAHb1"1. 2. 8b1pa)f(aeMoe 111M OTHOWeH111e. 3. C KaK111M naAe)f(OM ynoTpe611eH? Co103a. 1. npOCTOif111111111 COCTaBHOif1. 2. CoY111H111TellbHb1"111111111 noAYll1H111Te11bHb1"1. 3. CoeA111Hs:ieT Y11eHb1 npeAJ10)f(eH111s:i 11111111 YacT111 CllO)f(HOro npeAJ10)l(eH111s:i . 4. 8b1pa)f(aeMble 111M OTHOWeHll1Sl. MeJK.QoMeTHR. 1. nepBll14HOe 11111111 npOll13BOAHOe (B TOM 4111Clle COCTaBHOe). 2. nepeAaBaeMble 111M 3MOU,1110HallbHblif1 OTTeHOK, no6~eH111e. Cnosoco'leTaHHR. 1. 8b1Ae11111Tb CllOBOCO'ieTaH111e 1113 npeAJ10)f(eHll1Sl . 2. YKaaaTb HaYanbHYIO ¢opMy. 3. 8b1Aellll1Tb rnaBHOe (3HaKOM x ) 111 3aBll1Cll1MOe CllOBa (yKa3aTb CTpellKOill) . 4. OnpeAe11111Tb T111n no xapaKTepy rnasHoro c11osa (rnaro11bHOe, 111MeHHoe, HapeYHoe) . 5. OnpeAe11111Tb rnn css:ia111 (cornacosaH111e, ynpas11eH111e, np111Mb1KaH111e) . 6. YKaaaTb rpaMMaT111YecK111e cpeACTBa css:i3111 c11os (oKOHYaH111e, npeAflor) . 7. OnpeAe11111Tb xapaKTep CMblCllOBblX OTHOWeH111"1 Me)f(Ay c11osaM111 (onpeAe11111TellbHb1e, 06beKTHb1e, o6CTOSlTellbCTBeHHble) . npoCTOrO. OnpeAe11111Tb rnn npeAJ10)f(eH111s:i : 1. no U,ellll1 BblCKa3blBaHll1Sl (noseCTBOBaTellbHOe, no6yA111TellbHOe, sonpoc111TellbHoe) . 2. no 3MOU,1110HaJlbHOif1 OKpaCKe (BOCKJ1111U,aTellbHOe, HeBOCKJ1111U,aTellbHOe) . 3. no CTPYKTYpe : a) no COCTaBY rnaBHblX 'illeHOB (ABYCOCTaBHOe, OAHOCOCTaBHOe) ; yKa3aTb Tll1n OAHOCOCTaBHOro npeAJ10)f(eHll1Sl (onpeAe11eHHo-11111YHOe, HeonpeAe11eHHo-11111YHOe, o6o6~eHH0-111114HOe , 6e3111114HOe, Ha3blBHOe) ; cnoco6 Bb1p~eH111s:i rnasHoro YlleHa; 6) no HaJ11114111IO 11111111 OTCYTCTBll1IO BTOpOCTeneHHblX YlleHoB (pacnpocTpaHeHHOe 11111111 HepacnpocTpaHeHHoe); B) no nOllHOTe COCTaBa (nOllHOe 11111111 HenOllHOe) ; yKa3aTb npony~eHHble 411eHb1 ; r) OCllO)f(HeHHOe 11111111 HeOCllO)f(HeHHOe (06pa~eH111eM , BBOAHblMll1 CllOBaM111 , OAHOPOAHblMll1 , 06oco611eHHb1M111 Y11eHaM111 , cpaBHll1T8llbHblM o6opOTOM) . 4. 06bSlCHll1Tb nocTaHOBKY 3HaKOB npen111HaHll1Sl. CnoJKHoro. 1. Bb1Ae11111Tb ero YaCTll1 , OTMeTll1Tb 111X rpaHll1U,bl. 2. noKa3aTb rpaMMaTll14eCKll1e OCHOBbl B Ka)f(AOif1 YaCTll1. CnoJKHoco'IHHeHHoro. 1. OnpeAellll1Tb cpeACTBa c111HTaKc111YecKoill css:i3111 : Ha3BaTb COI03, yKa3aTb ero Tll1n no 3HaYeHll1IO (coeA111H111Te11bHb1"1 , nporns111TellbHb1"1) , no CTPYKTYPe (OA111H04Hblill, napHblill) , no cpyHKU,111111 (OA111H04Hblill , nosrnps:i10~111illcs:i) . 2. 06bSlCHll1Tb nocTaHOBKY 3HaKOB npen111HaHll1Sl . 3. Cocrns111Tb cxeMy. CnoJKHonop,'IHHeHHoro. 1. YKaaaTb rnasHoe 111 np111AaTOYHoe. 2. Ha3BaTb, YTO nos:icHs:ieT np111AaTOYHoe: rnasHoe npeAJ10)f(eH111e B u,ellOM 11111111 OTAellbHOe ero CllOBO (yKa 3aTb YaCTb pe4111 3TOro CllOBa). 3. 0TMeTll1Tb, Ha KaKoill sonpoc OTBeYaeT np111AaTOYHas:i YaCTb 111 KaKOBO cpeACTBO Cll1HTaKC1114eCKOll1 CBSl3111 (COI03, COI03HOe CllOBO). 4. OnpeAe11111Tb T111n npocToro npeAJ10)f(eH111s:i (onpeAe11111TellbHOe; 1113bSlCHll1TellbHOe; o6CTOSlTellbCTBeHHOe: MeCTa, speMeHll1 , CTeneHll1 111 o6paaa AeillcTs111s:i , np111Y111Hb1, u,e11111 , ycTYnK111 , yc11os111s:i , c11eACTB111s:i ; cpasH111Te11bHoe ; np111coeA111H111Te11bHOe, conocTas111Te11bHoe). 5. 06bSlCHll1Tb paccTaHOBKY 3HaKOB npen111HaH111Sl . 6. CocTas111Tb cxeMy. 6ecco103Horo cnoJKHoro. 1. OnpeAellll1Tb CMblCllOBble OTHOWeHll1Sl Me)f(Ay YaCTSlM ll1 (OAHOBpeMeHHOCTb, nOClleAOBaTellbHOCTb, npll14111HHO- ClleACTBeHHble OTHOWeHll1Sl , yc11os111e 111 AP -). 2. YKaaaTb rpaMMaT111YecK111e cpeACTBa, Bb1p~a10~111e OTHOWeHll1Sl Me)f(Ay YaCTSlMll1 (111HTOHaU,111Sl , nopSlAOK ClleAOBaHll1Sl YaCTeill 111 Ap .) . 3. 06bSlCHll1Tb paCCTaHOBKY 3HaKOB npen111HaH111Sl . 4. CocTas111Tb cxeMy. npeltf10JKeHHR C npRMOH pe'l&IO. 1. HaasaTb c11osa asrnpa 111 nps:iMylO pe'ib. 2. OnpeAe11111Tb 111x pacno11o)f(eH111e no OTHoweH11110 APYr K Apyry. 3. 06bSlCHll1Tb paCCTaHOBKY 3HaKOB npen111HaHll1Sl. 4. CocrnBll1Tb cxeMy. 5. Paao6paTb OTAellbHO KaK npeAJ10)f(eH111s:i c11osa asTopa 111 nps:iMy10 pe'ib. © 000 «VlHcponnacT», 2007 r. r. MocKsa, Kaw111pcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru 0 00 00
0 S P A 3 0 B A H 111 E HH.!!!9_nlACT 100 ~'!> CMCTEMA MEP MBECOBto;,'VOll -·EAMHMl.lbl, AOnycKaeMble K npMMeHeHMIO OcHOBHbie eAMHMl.lb• HaMMeHoeaHMe Ha11MeHoeaH11e 06o3Ha'leH11e HapaeHe c eAMHM4aMM Cl/I: Be/lM'IMHbl Merp - eAlllH1114a AJllllHbl K111norpaMM - eAlllH1114a MaCCbl ,l1m1Ha ceKYHAa - eAlllH1114a BpBMBHlll Macea aMnep - eA111H1114a Clllflbl 3flBKTp1114BCKOro TOKa BpeMR MOnb - BAlllH1114a Ko111114ecrna Bel1jecrna Cima 3neKrpw1ecKoro TOKa KaHAena - eA111H1114a c11111b1 csera TeMneparypa ,QonO/lHMTe/lbHble eAMHMl.lbl C111na csera paAt11aH - SA111H1114a nnocKoro yrna crepf1A111aH - eAlllH1114a TSflSCHOro yrna npOM3BOAHble eAMHM4bl npocTpaHcTea M epeMeHM HaMMeHoeaHMe HaMMeHoeaHMe 0603H3'1BHMB ee/lM'IMHbl PyccKoe Me>KAYHap. nno114aAb KBaApaTHblH MSTp M2 m2 06b8M Ky611148CKlllH MSTp M3 m3 CKopocib MSTp B ~SKYHAY MIC mis YcKopeHue M8Tp Ha CBKYHAY MIC2 ml s2 B KBaApaTe '-lacrora nep110A.npo4ecca rep4 r1.1 f;lz '-lacrora apa114eH11R CSKYHAa B MlllHYC c-1 s- 1 nepeoi.1 CTeneH111 YrnoaaR CKOPOCTb paAlllaH B CSKYHAY paAfc rad/s Yrnoaoe ycKopeH11e paAlllaH Ha CSKYHAY paAfc2 radls2 B KBaAPaTe nepUOA CSKYHAa c s npoM3BOAHble eAMHM4bl MexaHM'teCKMX eenM'IMH nnoTHOCTb KlllJlOrpaMM Ha Kr/M3 kglm3 Ky611148CKlll~ MSTp YAenbHblH 06bBM Ky611148CKlllH M8Tp M31Kr m31kg Ha KlllJlOrpaMM 11MnynbC KlllflOrpaMM-MeTp Kr•MIC kg•mls (KOflff'iBCTBO AB11JKBH11fl) B CBKYHAY Cuna, aec HblOTOH H N YABnbHb/H aec HblOTOH Ha HIM3 Nlm3 Ky611148CKlllio1 MSTp !laaneH11e nacKaflb na Pa Pa6ora, 3HeprnR A>KOYflb A>t< J M01l4HOCTb BaTT BT w noaepXOCTHOB HaTRJK8Hl18 HblOTOH Ha MeTp HIM Nim /111HaMl1'1BCKaR BR3KOCTb nacKaflb-CBKYHAa na·c Pa·s K11HeMarn4ecKaR KBaApaTHbli.1 MeTp M2/C m2/s Bfl3KOCTb B CBKYHAY npoM3BOAHble eAMHM4bl TennOBblX eenM'IMH Konu'lecrao rennOTbl A>KOYflb A>t< J YAenbHOB Kon-ao A>KOYflb A>KIKr Jlkg rennorb1, YASnbHblB rennOTbl nnaeneH11fl, napoo6pa3oeaH11fl, cropaH11R ronnuea YAenbHaR rennoeMKOCTb TeMneparypHbli.1 S'lpKOCTb CTlllJlb6 anocrn11b6 0CBBL1jBHHOCTb cj>OT Ha KlllflOrpaMM A>KOYflb Ha KlllflOrpaMM-KSJlbBlllH KSJlbBlllH B MlllHYC c6 ac6 cp HaMMeHoeaHMe 06o3Ha'leHMe MHo>K11re11b npMCT3BKM pyc. MBJKA. 3KCa 3 E 1018 nera n p 1015 repa T T 1012 rnra r G 109 Mera M M 106 Kl1nO K k 1a3 reKro r h 1a2 ABKa Aa da 101 ABLJl1 A d 10-• caHrn c c 10-2 Ml1nnH M m 10-3 MVIK{XJ o~ 0-g sb 1'104 Kp/M2 asb ~0,323 Kp/M2 ph 1•104 flK HaMMeHoeaHMe MHO>KMTem1 KBlllHHlflfllllOH KBaAPlllflfllllOH TplllflfllllOH MlllflfllllapA MlllflfllllOH TblCR4a CTO AeGRTb OAHa COTB.R OAHa AOCRTB.R eAMHMl.lbl PyccKoe MeJKAyHap. 3eyKoaoe AaaneH111e nacKanb MeTp M m na Pa KlllJlOrpaMM Kr kg CBKYHAa c s aMnep A A KBJlbBlllH K K KaHASfla KA cd MOJlb MOJlb mol Macea TOHHa T BpeMR MlllHYTB MlllH min 4ac 4 h CyTKlll CYT d nnocK11i1 yron rpaAyc, 0 MlllHyTa, CBKYHAa paA111aH PaA rad reKTap ra ha f1111Tp fl I KOSrjxf!114eHT nepsoi.1 cTeneH111 npoM3BOAHble eAMHM4bl 3neKTPM'leCKMX .. MarHMTHblX eenM'IMH HaMMeHoeaHMe HaMMeHoeaHMe ee/lM'lMHbl nnOTHOCTb aMnep Ha sneKTp11'1BCKOro TOKa KB. MSTP Kon-so sneKrp114ecraa, KyflOH 3nBKTp11'1BCKl1H 3apflA noaepXHOCTHaR nnOTHOCTb KynoH Ha ::in. 3aPRAa KB. MBTP 3n. HanpRJKBHl1B, BOJlbT ::in. nOTBHljl1an, pa3HOCTb ::in. nOTBHljl1anOB, 31/C HanpflJKBHHOCTb ::in. nonR 0011bT Ha MeTp 3neKTPl1'1BCKafl BMKOCTb cpapaA A6con10THafl cpapaA Ha MeTp A113neKrp114ecKaR npOHl1ljaBMOCTb, 3n. noCTORHHaR 3neKTp11'1BCKOB OM conporneneHue YAenbHOe Sn. OM-MSTp conporneneH11e 3n. npOBOA11MOCTb ClllMSHC MarHvtTHbli.1 noroK se6ep 11HAYKTHBHOCTb reHp111 MarHl1THMI 11HAYKLJ11fl Teena A6con10rHaR MarHl1THaR reHp111 Ha MeTp npoH114aeMOCTb, MafHUTHaR noCTOflHHafl A>KOYflb n p 10-12 cp f 10-15 ano a a 10-18 EAMHM4a AJlMHbl 06o3Ha'leHMe SAMHM4b1 M11Kp0M8Tp HaHOMBTp aHfCTpeM pyc. Me>KA· MKM µm HM nm A A 0603H3'l8HMe PyccKoe MeJKAyHap. NM2 Nm2 Kn c Kn/M2 Clm2 B v BIM V/m <t> F <t>IM Flm OM n OM•M n•m CM s 86 Wb r H T T r /M Him OAHa KBlllHT111111110HHaR MHOlKMTB/lb 10-5 M 10-9 M 10- 10 M f111KOMBTP nM pm 10-12 M 11KC-BA11Hl1lja lllKC-BA. x 1 , 00206·10-1 3 ~ 10-13 M cpM Im 1 (cpeMTOMeTp) = 10-15 M Ceeroeoii roA - paccTORH111e, npoxOAMMOe cseTOBblM ny40M B Te4eHMe OA- Horo rap.a. napceK - paccTORHl<S C KOTOporo P<JAMYC Op6MTbl 3eM/1M BMABH nOA yrnoM, pas bl OP,HoH ce " AB.
TeMneparypa L./enbCl1R, rpa,qyc oc oc pa3HOCTb reMneparyp LjenbCVIR HaMMeHoe. EAMHM4a 3Ha<1eHMe eenM'IMHbl H8MMeHOB8HMe o6o3Ha'leHMe a eAMHM48X Cl1 pyccKoe Me>KA. AflV!Ha aHrcrpeM A A 1·10- 10 VIKC-9AVIHV14a VIKC-0A x 1 00206·10- 13 M caHrnMerp CM cm 1:10- 2 M Ka6enbTOB K6 185,2 M acTpOHOMVIY0CKaR a.e. 1,496•1011 M 8,Qk:lt:Hdl,a CB9TOBOi.i rDA CB. rOA l.y. 9,4605•1015 M napceK nK pc 3,086•1016 M nnollja,qb KBa,qpaTHbli.i CM2 cm2 1•10-4 M2 i;attik:ltia~IIJ ap a a 100 M2 reKrap ra ha 1•104 M2 Ql:i:t!!lM ts~011~~Q~l1~ QM3 Q[]3 l•l Q-6 M3 caHrnMerp nvirp n 1·10-3 M3 Macca rpaMM g 1·10- 3 Kr arOMHaR BAV1Hvi4a a.e.M. u 1,6605·10- 27 Kr MaCCbl (yrnepOAHaR WKana) 2•10-4 KrKaQaT M0TQ1114eCKll1~ Ka(2 ct 4eHTHep 4 g 100 Kr TOHHa T t 1000 Kr 61J~fii18 ta:U:ll:l;!Ia Mldtl rnio 60 ~ YaC y h 3600 c CyrKVI cyr d 86400 c nnoCKVli.i yron C9KYHAa =4,85·10- 6 pa,q MVIHyra =2,91-10- 4 P3A rpa,qyc =0,0175 P3A 0(.l8MC~ ;![CD l 5Z llaA nonHbli.i yron 06 6,28 pa,q (o6opor) JlVIH9i.1HaR caHrnMeTp B CSK CMiC cmi s 1·10- 2 Mi C Cls:CIJCCib ~li:HJCMBIIJ a :tac ~M& ~[!]/b Q 2ZB !.!I~ y3en (MOpCKOi.i) y3 kn =0,514 Mi C KVlnOMere B CSK KMiC kmis 1000 MiC n111Hea'.1H08 caHTYIM0Tp Ha CMi c2 cmi s2 Mo-2 Mi c2 ~CKOpeHvie CeK~HAY B KBa,qpare 4acrora o6opor e CBKYHAY o6ic 1 c 1 Bpallj9HVIR o6oeor e MviH~T~ 06iM 1/60 c-1=0,0167 c- 1 nnoTHOCTb reaMM Ha KZ'.6VIYBCKV1i.i r/CM~ 9ism~ 1•1 o~ KriM~ caHrnMerp Cvina 8VIHa 8VIH dZ'.n 1·10- 5 H MexaH•YeCKoe KvinorpaMM-cvina Krc/MM2 kgf/mm2 =9,81 ·106 na HanpR)!(9HVl0 Ha KB. M'1nn'1M9TP AaeneHvie A•Ha Ha KBa,qpaTHbli.i AVIHiCM2 dyni cm2 0,1 na caHrnMerp T8XHW-18CKa~ am at =9,81-104 na aTMOCcpepa KrcicM2 kgf/cm2K'1norpaMM-C'1na Ha =9,81-104 na KB. CaHTVIM9Tp cpV13VIY9CKaR amM atm 101 325 na (HOpManbHaR) aTMOCcpepa M'1nnviMeTp BOARHOro MM BOA.CT. mmH20 =9,81 na CTOn6a t.a1i:iam:n.1eIP IJI~Il:iQCQ Mt.a IJI CI [!][!] Clg =l33 3 Da cron6a 6ap 6ap bar 1·105 1la Pa6ora, 3pr 3pr erg 1-10-7 A)!( 3HeprviR san-Yac BPY W·h 3600~ K1o1nosarT-Yac KBPY kW•h 3,6•10 A)!( CTapb1e pyccKMe eAMHM4bl 111 111x nepeeoA e eAMHM4bl Cl-1 1 a.e. (acrpOHOMVIYeCKBR 0AVIHV14a) = 1,496•1011 M 1 CB. rDA (cBeTOBoi.i roA) = 9,463•1015 M 1 nK (napceK) = 3,086•1016 M = 3,26 ceeroeoro roAa HeK0Topb1e APeBHepyccKMe Mepbl AecJtTMHa (Mapa 3eMenbHoi.i nnol!13A") - 0 ,9 ra. Kynb (Mapa CbmyYvix ren) - AllR p>t<vi - 151 ,5 Kr, Anl1 ceca - 100,3 Kr. JloKOTb (Mepa AnVIHbl, paeHaR AnviHe noKreeoi.i Kocrn) - 45,5-47,5 CM . CalKeHb KOCaJt {Mepa AnV!Hbl, paeHaR paccroRHVllO or nanb4ee neeoi.i Horn AO KOH4a nanb4ee npaeoi.i pyKvi, BblTRHyroi.i no A"aroHanvi) - 216 vinvi 248 CM. CalKeHb npocTaJI (Mapa AnVIHbl, paeHaR pa3Maxy pyK or KOH4oe nanb4ee OAHOi.i PYKVI AO KOH40B nanb4ee APYrD) - 152 vinvi 176 CM. EAMHM4bl AfllllHbl M11nR MopcKaR MVlnR Ka6enbroe S'lp,q <llyr At0i.1M 5onbWaR nVIHVIR ManBJI nMHMR EAl<IHM4bf CKOpocTM 1,609 KM 1,852 KM (TOYHO) 185,2 (TOYHO) 914,4 MM (TOYHO) 304,8 MM (TOYHO) 25,4 MM (TOYHO) 2,54 MM (TOYHO) =2.12 MM <llyT B C0KYHAY =-0.30 C M'1rui a Yac = 1,609 KM. Y:ren 1,852 (MOPC'<lll' Kll" e ac =O 5 c EAMHM4bl nno1J48AM AKp =4046,9 M2 Kea,qpaTHbl~ APA =0 ,836 M2 Kea,qpaTHbl~ cjJyr =929 CM2 KBBAPBTHbl~ AtOi.iM =645,2 MM2 K ea,qpaTHal1 nVIHVIR =6 ,45 MM2 (6onbWaR) EAl<IHM4bf 118CCbl ToHHa (An"HHBJI • =1 ,01 6 T TOHHa (KopoTKBJI ,.Q,907 T l.leHTMep HHb6i) =50.8 l.le+m<e!J ( KOOOT!OOI) "'45.4 Kr =453.6 r 373,2 r 3n0KTPOBOnbT KMnorpaMM-C'1na- -Merp 3B Krc·M eV kgf•m =1,602·10- 19 A>t< =9,81 A)!( Ha11MeHoe. eenM'IMHbl MOUJHOCTb noeepxocTHoe HaTR)!(8H'1e MoMeHr C'1nb1 il1HTeHC'1BHOCTb B03Ayxa KonMYecreo rennoTbl EAMHM4'1 H8MM8HOB8HMe o603Ha~eHMe 3H8'19HM8 e BAMH114ax Cl/I nowa,q'1HaR cvina KMnorpaMM-C'1na- M0TP B CSKYHAY AMHa Ha caHTMMerp A'1Ha-caHrnMerp K'1norpaMM-C'1na- 3pr e ceKYHAY Ha KB. CBHT'1M0Tp 3pr pyccKOB MBlKA· 3eric ergis n.c. KrC•M/C AMHiCM AVIH•CM KrC•M 3pri c•cM2 3pr Kan kgf·mi s dyn/cm dyn·cm kgf·m =736 BT =9,81 BT Mo-3 Him HO H·m =9,81 H·m erg/c•cm2 1•10-3 Br/M2 erg 1.10 A)!( Kanop'1R KVlnOKanOp'1R KKan cal =4,19A)!( kcal =4,19·103 A)!( YAenbHaH Kanop"" Ha rpaMM Kan/r cal/g =4,19·103 A>KiKr rennora nnaeneHHH, wenbHaH rennora napoo6pa30BaHVIH, YABnbHaH rennora K"1JlOKa11op111H Ha K'1norpaMM 3pr Ha rpaMM KKaniKr 3pr/r kcal/kg ergig cropaHt1R tonm10a YAenbHbl~ pacxoA ronnviea YAenbHa" rennoeM KOCTb seuiecrna rpaMM Ha nowa,q. r/n.c.•Y =3,78·10- 12 Kr//1>1< CMny B YaC 3pr Ha 3pr/r•°C ergi g•°C =1·10- 4 A)!(fKr•K rpaMM-'P3AYCl.lenbCVIH Kanoe•si Ha Kanir•°C cal/g•°C =4,19•103 tJt</Kr•K c11111a toKa Kon1o1Yecreo 3neKTp'1Y8CTBa 3AC. pa3HOCTb noreH4'1anoe, 3n. HanpR>KSHM0 HanpR)!(SHHOCTb 3n0KTP'1Y9CKOro 3n0KTp11Y9CKOe conpOTlllBJl0Hlo10 rpaMM-rP3AYC l.lenbCVIR KHJ10KAn0PHR H8 KKahlKP c KVlnorpaMM-rP3AYCl.lenbCVIH 8All1Hl114a Cll1hbl TOKa Ci c eA. 3apRAa ere BA. 3.a .c. CIC; 8A'1HV14a pa3HOCTVI noreH4vianoe CIC; SA. HanpR)!(8H'1ll ere SA. HanpR)!(SHHOCT'1 ere 3n. SMKOCTVI CM cm 0A. 3n. COnpOrnBnBH'1R CIC ==3,33•10 19 Kh =3,33·10- 1°Kn =300 B =3•104 Bi M 8,99•1011 OM= =9·1011 OM YAenbHOe 3n0KTpVIY9CK00 conporll1BileR111e 3neKTPMY9CKaR npOBOAMMOCTb OM - KB. 0 M•MM2 /M O•mm2 i m MMnnMM9Tp Ha MeTp eA.YA.3n.conp. CIC eA. 3n. npos. ere 1•10=o OM·M 8,99·109 OM·M= ==9•1Ug OM•M YAenbHaR 3Jl9KTpV!Y0CK~ HPOBOAAMOCTb MarHVITHbli.i MarHVITHaR @AYkll~R HanpR>t<0HHOCTb MaFHIATHOfO hbhs:i 3neKTp'1Y9CKall 3HeprMR SA. YA· 3n. npoe. ere 0A. MarH. noTOKa ere MKC Mx SA. MarH . MHAYK4MM l e Gs c1 c raycc) SA. Hanp. Marn. non" 3 Oe Cl C (3pcteA) 3pr 3pr erg Ho-0 Bo 1·10- 4 T =79,6 AIM EAMHM4b106beMa, eMeCT'1MOCT'1 EAMHM4bl AflMHbl Ky6viYeCKBR n'1HVIR =16,4 MM3 TOYKa 0 ,254 MM nviHVIR 2,54 MM Ky6VIY0CKVI~ AIOi.iM = 16,4 CM3 At0~M 25,4 MM BepwoK 44,4 MM Ky6VIY0CKM~ eepwOK =87,7 CM3 <llyT 304,8 MM ApWVIH =71 ,1 CM WrocjJ (1 / 10 BSAPB) =1,23 n Ca)K0Hb =213,4 CM lapHe4 3 ,28 n BepcTa = 500 Ca)!(0HRM=1500 apWVIHBM=1066,8 M BeApO =12,3 n Ky6VIY0CKV1i.i QJYT =28,3 AM3 4erneprb 0 ,21 M3 (AnR CblnYYMX Ten) 4ernepviK Ky6viY. apwviH Ky6viY. YH4MR ApaxMa (AHrnMR) lpaH EAl<IHM4bl o6'bE!M8, BMecTMllOCTM =28,35 r =1,77 r =64,8 Mr TOHHB perncrpOBBJI =2 ,8M3 Ky6'140CKMM l1PA =-0.76 M3 Ky611Y0CK"1M ¢ YT =28,3 AM3 Ky6Vl4ecKMi1 A!Ot<M =1 6 ,4 cM3 5 yuiellb (AHm"") c=36,4 n 5ywem. CWA) >=35.2 n r~ < ..... =4 5 11 r aI1110t< cyxciM CWA) =4 4 n il-1'a ( =568.3 EAMHM4bl MSCCbl AonR =44.4 Mr <llyHT=96 30n. =409,5 r 3onOTHVIK =4 ,27 r nyA=40 cpyHTBM=16,4 Kr nor = 12,8 r 5epKoee4 =163,8 Kr CyxaR nVIHTa (CWA) :>KMAKOCTHBR nVIHTa (CWA) lannoH )!(MAKOCTHbl~ (CWA) 5appenb H0QJTRHO~ (CWA) "1H<PoPMB!jMOHHO-CnpaB04HBR ra611H4a ~ 000 ""111¢onnacr•, 2004 r. MocKBa. KB111HpcKOe wocce, 21 =550,6 Mn =473,2 Mn =3,8 n =159 n 00 00 "'0
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<l>K3K'leCKaJ! MaKpOCKOnH'ieCKOe Teno CHCTeMa MaTepHanbHaJ! TO'll<a OIDlchrnae- CocTOl!HHe noKOJ! .IJ:emKeHHe Moe J1eneITT1e llJill paBHOMepHoro c ycKopeHHeM rrpKMoJIHHeHHoro )lBIDKeHHJI CKcTeMa 11eyx Ten CHCTeMa llBYX MaTepHanbHblX TOtJ:eK CYTb 3aKOHa nocrynHpyCT cymecreoerurne HHep111rnJIDHOii CHCTeMbI OTCqeTa BJaHMo.n.eHcTBHe C11nb1 )leHCTBHJI 11. nponrno- orrpeiienRCT K3MeHe- 11eiicreHJ1 paBHhl no MOllYJIIO. Riie CKOpOCTll, T.e. IlpoTHBOilOJTOllCHbl no Ha- ycKopeHHe rrpaBneHHJO, rrpHJioJKeHbl K (ecm•IF=O , To a=EF v= const) m pa3Hh!M TenaM, O)UIOii rrpH- pO.D;bl ft:.2 =-.F21 CTpKMepb1 .ll.BH'IKeaHe KOCMH- J:(eH>KeHHe nnatteT~ B3aHMo.u.eHCTsHe Ten: Co;m- npoJ1BneHHJ1 qecKoro Kopa6mi na11ettHe Ten sa na H 3eMJIH, 3eMJTH 11 JlyHhI, BllaJIH OT rrpHTRrH- 3eMJTIO, TOpMOJKeHHe aBTOM06HJTR H noeepXHOCTH eaiom11x Ten H pa3roe aBTOM0611- 3eMJTJI, 611JIDJ1p1lHb!X rnapoe J1R fpaHHnbI l1HepUHanbHb!e CHCTeMbJ OTCqCTa npKMettH - MaKpo- 11 MeraMHp MOCTH BIDKCHHe co CKO OCTJIMH, MBOro MCHbID.HMH CKO OCTH ceera C~na , pa60TB, 3Hepr~H <llopMyna rpatJ>e1< Cwra TJ!lKeCTH ~Fr =mg mg "' 0Q. " Pa6oTa CWlhl TJ!)l(eCTH.. ~ .. A=FScosa; F=mg; S=hQ mg =.. a=O; A=mgh 0 ~ :.: IloTeH.llHanbHaJ! 3eeprn.>I mgHf·------ . . =... EP =mghQ. " 0 : h..Q H = KH:ee-r11qecKaJ1 3HeprHll EKL h"3 mv2 Q Q. EK=- =mg(H - h)IQ 2 0 H-+Q 5 IToJTHax 3HeprHll :G... mv2 E=mgh+-=mgH 2 H t Cima yrrpyrncTH r F;f ~2 IQ Fx =-kx... Xi -x ~ =,., Pa6om CHJlbl ynpyroCTH ~f l kxi kx2 X2 •e: ="' A=-zx1-2X2 Xi x J: "= ITOTeHI.HanbHax 3Hepr11.>J EJ ..t; kx.2 ',., Ep=2 : " x, x..: Xi..: Q l<HHCTH'leCKaJ! :meprH.>I= EJ .. mv2 k 2 2"'... " EK =1=2(x, -x, ) x, xe: Xi'2e: ITOJTHaJ! 3aeprHJ1 EJ Q :.: kx2 mv2 kx2Q : " E=-+--=-i " x, x... 2 2 2 Xi Ha'laJJbHble ycnoee11 Onacauue Jl,BH*'.eHHR Raqam,HaJ[ Haq3.TlbffasJ lj>opMYllbI TPaeKTopHll KOOpllHHaTa cxopOCTh Yo=h Y:1 j;~o v=-gt tigt2 y=h-- 2 0 x Yo=h y:~. v= - v0 -gt l~ gt2 y=h-v0 t-- 2 0 x Yo =0 y~g V=V0 -gt 'll~ gt2 y= v0 t--- 2 0 x 0 x Yo =0 y~ v. = v0 cosa :oVo lg v, = v0 sina- gt x= v0 tcosa a t' 0 x y=v0 tsina - L 2 Yo =h ye V, =V0 y~ VO Yo lg Vy =-gt X=V 0( ' :.. v v, 0 x gt2 0 xy=h-y Yo= R1+h y u. =u0 cos a. Vo =0 Yo ~ u, =v0 sina. ,,.,. ... -h ' 'Xo h . 2rc / x = (R3 +h)slilTt I R, a VoVo =8KMlc I u:1I Y: I R1~ 2rc I 0 ,,__ / vx0 x y = (R3 +h)cosTt ' CTaTMKa l13Y"aCT ycJJOBH.>J paBHOBeCJlll TBep.zu,rx Ten BM)l,hl PABHOBECID! YcroiPrneoe Ee3pa3JJH'!HOe ~CPEACTBA OIIl1CAHIDI Mo.n;eJTb Tena s CTaT11Ke - a6coJ1K1Tuo Teep.n;oe Teno. ' ___.... HeycToii'lHBoe ~ Ce11Jb - npenllTCTBHe JI;BIDKeHHJO Terra: rroeepXHoCT&, eepesxa H T..n;. / / PeaKUHH CBll3H - Cl!Jla, .n;eikTBYJOIUaJ! Ha Teno co CTOpOHbl CBJl3H, no HOpMaJTH K aanpaenemno BOJMOJKHoro nepeMe1.11eID1.J1. MoMeHT c11nhi - M=±Fd, r.n;e d - nneqo CHnhi 0 3&KOH Ka1<oea MaTeMaTH'lec - B K8KHX CHC- Tpe6oeaHHJ1 BuyrpeuuHe ff3eecTub1 JIH coxpaueHHJ1 CK:8SI 38IlHCb 38K'OH8 TeMaX OTC'leTa K suemHHM CHJJ&M, BLJHOJIHHCTCH 11eiicTBYKIUIHM Ha 3SKOH CHCTeM}' 3aKOH L,mv = const B coxpaHemrn ll:mo,= OOMI HHepnHanbHblX HMll)'Jl.bCa L,mvY= const L.F = O L.mv, = const JaKOH EK+ Ep = const B coxpatteHID! C'' HReprrHanbHblX ::mepnrn - 2 - +mgh = const l:A=O mv2 kx2 - 2 - +- 2 - = Const 33.KOH L=const B COxpaHeHID! fro=COnst I~ ~.! =0~OMeHra llDlll)= mvr= CHJJbl, 11eiiCTeyK1111ee B CHCTCMeTeJI .J1J06bre KoHcepeaTKBllbie (nOTeHUHaJTbHhle) ~CBJILI TJ!rOTeHHJI CH.Thi ynpyrocra I ;lioiiwJ,m CJlf'l&H uapy- lllCHH_H 38KOHOB coxpaeeuea He-r He-r HeT ITpHinum MHHHM)'Ma noTeH.J.lHanbROii 3HeprnH I Y u lCTQff"qHBQ TO ITOJIQ)f(CHHe Tena, B KOTOpOM ero DOTeH- UJlanb!laJ! :mepmll KMeCT eaHMeHbrnee 3Ha'lemie H3 ecex B03MO)l(Hh!X MH</JopMaljHOHHo-cnpaeO'/Ha• Ta6nHllB © OOO•MHljJoonacr•, 2007 r Moa:Ba. Kam.<pacoe wocce.21
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Hn1eueHHe lbMeueuee lbMeneHHe Mo.~•puu 8blpllll(eHHe rpafjlRKR Hueauee MaTeMBTH'lecKoe Iloey'lenue Coeepweuue TennoeMKOCTb Bblp8ll(eHHe o6'beMa KOJIR'lecTRB pa60Tb1 (A) euyrpeuueii Te11meparypb1 (D.U) nepeoro ua'lana 38BHCRMOCTR npouecca npouecca (D.V) TeDJIOTbl (Q) '.)HepntR (6U) <t.n TepMO,l1HH8MRKR p(V) D.T A,nua6aTHbrH pV"=const >O 0 >O <O <O 'L0 A'=l'lU <O 0 <O >O >O 0 v f =const 0 >O 0 >O >O ~R l_LJifaoxopHbrii Q=l'lU 2 0 <O 0 <O <O 0 v >O >O >O 0 0 p~J.faoTepMH'!ecKHii pV=const 00 Q= - A' <O <O <O 0 0 0 v v >O >O >O >O >O .?_R 'l=113o6apHbtii - = const Q=l'lU +A' T <O <O <O <O <O 2 0 v "1Aea11bHblM ra3 TepMOA111HaM111YecK11111'1 MeTOA raJ - CHCTeMa MHKpO'!aCTJU~ r83 - M8KpOCKOITH'!eCKall CHCTeMa MO,!J,e.Jlb - TepMo,wrnaM.WieCKall CHCTeMa OcHOBHble ee11111Y111Hb1 Macca Moneicyrrbl m KoHU;eHTJ)llllWI MOJieKyn n Cpe.llHJlll KBa,ll,paTH'IBaJI CKopocTb V Cpe,ll,HJlll KHHeTHqecKaJI 3Heprmi Moneicyn E l.fucno MorreH. V MoJJJ1pHaJ1 Macca M IlocTOJIHHaJI liom.UMaua k 1 _ 2 1 _ 2 2 E- kT p=-nmv =-pv =-n =n 3 3 3 3 U=-vRT 2 IJ,eHTpbl CHMMeTpHH ('IBCTHllbl, 3 3 l'l.U =-vRl'l.T =-8.(pV) 2 2 0CHOBHble Be/1111'ill1Hbl Macca raJa m ~aBJielllie p 06'beM V TeMIIeparypa T IlJIOTHOCTb p BH)'TpeHIDIJI :mepntJI U MoJJJ1pHaJ1 Te[IJloeMKOCTb C YHHBepcanbHaJI raJOBaJI nocTOllHHaJI R m pV=vRT=-RT M OcHOBHble CBOHCTBB IlpHMepbl Ten KJIHCTanna o6pa:Jyiomee peweT1cy) Cunbl B3BHMO.l1eiicTBHll e KJIHCTanne KpRCT8JIJIOB MoneK)'JlllpHb!ii MoneK)'Jlbl Bau-.11ep-Baanbca, .11nnOJib-J1HnOJibHble, HuJKall TeMneparypa nJiaBJieHHll Ha<j>Tanuu BO,l10p0,!1Hble CBll3H HH3Kall TBep.llOCTb MeTaJIJIH'lecKHli IlorroJKHTeJibttble HOHbl 3rreKYpOM8IBHTHhle (MelKJIY 3JieKYpOHHh!M Bb!cOKall Jrrerrrpo- u TenJionpoeoJIHOCTb MeTaJIJibI ra30M " IIOJIOJKHTeJibHhlMH HOHaMH) KoeaneuTHblli ATOMhl HJIH rpynnbl aToMOB KoeaneHTHble CBll3H O<JeHb ewcoKaR TeMnepayYpa rrnaeneHIDl. AnMa3, KpeMHHH 0'1eHb 60JibWall TBep,ll,OCTb 11ouuhlli l1oHLJ (nonoJKHTeJibHble " 3neKYpOMarnHTHbie (MelKJIY HOHaMH) BMCOKall TeMneparypa nnaerreHHR. XpyrrxoCTb IloeapeHHall com. OYpHil8TeJibHble) 0THOClr1Te/1bHas:i B/18>KHOCTb B03AYX8 q>= f 100% Kan1r11111s:ipHOCTb Bb1c0Ta no.llbeMa )l(HJIKOCTH a Kan11JJJUipuoi1 Tpy6Ke h = 2cr cos e pgr TO'lKB pocbl - TeMnepaTypa, np11 KOTOpoil nap nepeXOJl!1T B COCTOllH11e HaCbJLUeH!1ll. noeepXHOCTHOe H8Ts:l>KeH1r1e F I :>i<H.uKOCTb cMa'IHBaeT ue cMa'IHBaeT noeepXHOCTb KailHJIJUlpa t.1H<j>OpM81.1110HHO- cnpaBO~H8ll Ta6n114a ©000 «1'1Hcj>onnacT», 2007 r. r. MocKaa, Kawi-ipcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru N '<I' 0 no,llnucaHO Bnf"laTb 14. 11 2008. T11pilJK 4000 JIG 3aKa3 N• 29242 113,llarenb 000 •l1Hl/JOfJllaCT•, MOCKB<l, KiJwupCKoe wocce, l 1 Ten. (495) 730-01-87. Tunorpaqm• 000 •8..,.,-Crap• 107023, Moc:ICBd, yn 3nenpo3aBOIJO<aff. 20
0 ~ 06PA30BAHME 3Ml111P111.JECR11iffiA3HC ~ OIIbITbI Kynotta, 3 pCTeAa, A~mepa, 0Ma, <llapaAell, MHmrnKetta - HocjJcjJe, MattAenbwTaMa - IlananeKCH TEOPETWIECR11if fiA3HC ~ &ean HJHpOBRHHblH OfrbCKThl : 3neKTPH'leCKHH 3apll.l, 3neKTPl!4eCKOe none, MarHHTHOe aone, eeweCTBO - CHCTCMa 3aplDKeHHblX qaCTifl.I, BJaHMO):eHCTBHe nocpeACTBOM noneii Ocuosuble nonHTHH: q, E, B, C, L, R, E, µ, c 0CHOBHble llJICH: B3afill O.UeiicTBHll, coxpaHe- HHll, OTHOCHTeJ!hHOCTH, 6mf3KOAeiicTBHll ~ Y paeHeHHll MaKceenna. 3neKTPOHHal! TeopIDI KoHCTattTb1: E0, µ0, I c- - ~eoµo .. 3aKOHhl 3neKTPOCTaTH4eCKOro llOJUI 3aKOHbI CTa1.vmHapuoro 3neKTpW1ecKoro DOJUI (aoCTOllHHbfH TOK) 3aKOHbl MarHHTHOro DOJUI 3aKOHbl 3neKTPOMarHHTHOro DOJUI (3aKOH 3neKTPOMarHHTHOH HHLYKl..IHH, aepeMeHHblH TOK) 3neKTPHqecKHe H MarHHTHbie CBOHCTBa BeweCTBa TeopHll 3neKTPOMarHHTHoro aoJUI .. IIPHMEHEHIUI 3neKTPOTex.ID11<a. PaAHoTelCffifKa. 3neKTPOHHXa. 3uepreTHKa .N'!.N'! CxeMa :meKTpH'leCKOH u.enH 3aKOH 0Ma 1 a R b I= Uab 0 CJ 0 R 2 a RJ R2 b I=~ o----e::J----CJ R1 + R2 Rl I=~ 3 ~ R,R22 R, +R2 4 Q e l =- - R +r 5 [I,";':"·'1 ne l= - - R+nr ,1e,r ::e,r e'I I=-- 6 n ......... ...... R-..!:..,1e,r I 'I n R •- a ~C:,r C:-L 0 0 I= - - r 3aKOHbl TOK3 3nerrpITTeCKHe uenu OcuoeH1>1e TeXHH'!ecKHe npHMeHeHHll 3,[( 3neMeHTbJ CTO I3nerrpocT3TH4ecKoe none I MarnHTOCTaTH'lecKoe none MarnHTHb1e OcuoBHLJe HHALI noneil xapaKTepHCTHKH rpaBHTaQHOHHOe 3JJeKTPOCT3TH'leCKOe 06beKTbl B33HMOAeiicTBHll Bee Tena H 'laCTHl..lbl 3apJDKeHHJ>Ie Tena H qaCTH Ubl <llopMynJ>I CHJ!hl F =G m,m2 F=kjq,jjq,j R' r2 HanpllJKeHHOCTb Fg=- - ft E=- m q PaJHOCTb noTeHUHanoe q>, - q>, =g(h, -h,) q>2 -q>1 = E(d2 -d1 ) Pa6oTa no nepeMewelililO A= mg(h, - h,) A= q(q>, -q>,) Tena HJJH 3apl!Aa A=mgh A=qEd Pa6orn no 3aMKHyroil A =O A=O TPaeKTopKH N•N• CxeMa JJICKTpn'lecKoii uenn J aBHCHMOCTb CHJlhl TOK& OT lfftCTOTbl R ~lI 0 c::::J 0 ' (i) 2 0 lie 0 ~t --' (i) L ~1"--3 ~ ' (i) ~~ ~t -4 ' (i) R 5 ~ ~t --- ' (i) R L ~t6 ~ ' (i) L ~t7 ~ - • (!) R L C ~t '"' I 8 ~ ~ (l) =-- '(!) 0 ..fiC O>o ~ ~t 1 9 (l) =-- _,,. 0 ..fiC ro. '(!) /+ I c. CO, = - - c .--ih - .[LC; I 6l 2 o--IH Cil <: Il --0 -~- = 11 ,1L(C1 - C1 )
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B11A11Mbli1 CBeT 3aH11Maer A11ana30H np116n11311renbHO OT 400 HM AO 780 HM 11n11 OT 0,40 MKM AO 0,78 MKM. 0,01 HM 0,1 HM 104 10-' 10-1 I I I3·1020 3·10 19 1 HM 10 HM 100 HM 1 MKM 10 MKM 100 MKM 1 MM 10 10 1 102 103 10• 10' 10• I I I I1 ii I I I I3·1017 I 3·10151 13·10" 3·10 12 1 I I I I 1 CM 107 I3·10 10 10 CM 1 M 10 M 108 109 10 10 I I3·101 IA, HM v, r~ Pa.QMoeonHbl PeHrreHoecKoe 1 1• Y<I> J>I ...,i,..._--'-11 "'-K--l>~I ,. • • nrteH•e I l> ) .._,_I--~------- faMMa-Many-teHMe I / ' 1-400 HM ~ 1-780 HM I 1~Cf3 )t<D: 1 I BMAMMblit ceer 0nTM'i8CKMM AM30330H PMCYHOI 2.6.2. WKana 3fl8KTPOM8rHHTHblX BOflH. (paHHljbl M8/K/lY pa3flH~Hb/MH ,4Hana30H8MH ycnOBHbl. Geer B OAHl1X OnblTaX 06HaPY>Kl1BaeT BOnHOBble CBOHCTBa, a BAPYrHX - KOpnycKy- nHpHble, 03HaYaeT, YTO ceer 11Meer cno>KHYIO ABOHCTBeHHYIO np11pOAY, KOTOpyto npl1HATO xapaKrep113oearb repMl1HOM 11opnyCKYJ11IPHO-BOJ1HOBOM AYBJIH3M. 1.8. C11upaJ11,1111e np•6opw. 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B QJOKanbHOH nnocKocrn nl1H3bl paccTOHH11e Ym OT MaKCl1MyMa Hyneeoro nopHAKa (m = 0) AO M3KC11MyMa m-ro nopHAK3 np11 ManblX yrnax Al1- 0 PMCYHOl 1.8.1. l/11rjJpaKliHR ceera Ha pewerKe. ctJpaKl1111 paeHo Y., =m} F , rAe F - QJOKYCHOe paccTOHH11e. AMllJpaKQMeM CBeTa H33blBaeTCff ffBneH11e OTKnOHeHl1ff ceera OT npHMOn11HeMHOro Hanpae- neHl1ff pacnpocrpaHeH11H np11 npoxo>KAeH1111 e6n11311 npenHTCTBl1~. P3A11YCbl Pm30H Cl>peHenH: A.2 P = p2 -L2 = mA.L+ m 2 - "' .JmA.Lm m 4 . TaK B OnTl1Ke A.« L, BTOPblM YneHOM nOA KOpHeM MO>KHO npeHe6pe%. Kon11Yecreo 30H Cl>peHenH, yKn3Ab1eaio11111xcH Ha R1 oreepcrn1-1, onpeAenAeTCA ero paAl1YCOM R: m =A.L . 3AeCb m - He o6A3arenbHO 4enoe Y11cno. Pe3ynbrar 11HrepctJe- peH41111 BTOp11YHblX BOnH B TOYKe p 3aBl1Cl1T OT Yl1Cna m OT- KpblTblX 30H Cl>peHenA. Bee 30Hbl 11Meior OA11HaKoeyio nno- 1113Ab: Sm= itp! -itp!_,= itA.L = S, . PMCYHDK 1.7.1. (paHHljbl JOH (fJpeHe- nR BnnOCKOCTH OT- eepCTl1R. A, >A, > A, > ... > A,,. rAe Am- aMnn11ryAa KOne6aH11M, Bbl3B3HHblX m-i:i 30HOM. A11ctJpaK4110HHb1e AeneHl1A npoABflAIOTCA Ha116onee OTYern11eo, KOrAa Ha npenATCTe1111 yK- R2 fl3AblBaeTCA fll1Wb He6onbwoe Yl1Cfl0 30H: m =LA.;:>: I 11n11 R' ;:>: L'),, . 3TO COOTHOWeH11e MO>KHO paccMaTp1183Tb K3K llPMTepMM H36JllOAeHMA AMllJpaKQMM. Ecn11 Yl1Cno 30H Cl>peHenH , yKnaAb1BatoU111XCff Ha npenHTCTBl111, CTaHOBl1TCff OYeHb 6onb- R' w11M, Al1QJpaK4110HHb1e HeneH11H npaKTl1YeCKl1 He3aMeTHbl: m= LA.>> I 11n11 R 2 >>L'A . 3TO Cl1flbHOe HepaeeHCTBO onpeAenHeT rpaHHQY npMMeHHMOCTM reoMeTpM'leCKDil onTMKM. Ta- Kl1M o6pa30M, reoMeTpM'leCKBA DnTMKa ABJIAeTCA npeAeJlbHblM CJIY'IBeM BOJIHOBOil DnTMllM. p PMCYHOl 1.7.2. 30Hbl (fJpeHenR Ha crjJep11~eCKOM rjJpOHTB BOflHbl. ,---;;-;- PacYeT AnA P3Al1YCOB Pm30H Cl>peHenH Ha cctJep11YeCKOM QJPOHTe eonHbl: Pm= Vm a+b ·L . - Y 1.9. non1p.ia1P1• cana PMCYHOK 1.9.1. npoXOIK,48Hl18 CB8T8 ~epe3 KPHCTann 11cnaH,4CKOrO wnara (,qeoiiHoe n~enpenoMneH11e). 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• • UH4'0n/ACT n.· www.infoplast.ru K11acc1r1cp1r1Ka41r1H Heconeo6pa3yt0L111t1e (6e3pa3I11t14Hb1e): N20, NO, CO? coneo6pa3yt0L111t1e OCHOBHble aMQJOTepHble Klt1CJ10THble I,II II-IV V-Vll MexOy MexOy HMexOy MexOy nepex. +7 Na20 ZnO co2 Mn20 7 Cao Al20 3 S03 c~o +3 +6 Cr2 0 3 Cr03 OKCIAA Cr(ll) OKCIAA Cr(111) OKCIAA Cr(VI) ra3 >K1t1AK. C02 H20 S02 so3 NO Cl20 1 N02 Me HMe <!>"13"1'-leCKMe CBOHCTBa TeepA. OCHOBHble aMQJOTepHble Si02 P20 s Cr03 MexOy (Lll•I Ll..1-3.) Klt1CJ10THble OKCIA,Qbl ~ +H 02 paCTBOp Me(OH)xJ. Hx03y Me30y! Me(N03)x (Mg-Cu) Klt1CI10THbl~ OKCIAA H2 0 -+ K-Ta (p.) Ll..lefl04b -- COI1b + HzO aMQJOTepHbl~ I H20 -- Llleno4b OCHOBHO~ OKCIAA Klt1CI10Ta 7 COilb + H20 H J... Me+ H 0? ? O,QHOocHOBHble MHOrOocHOBHb1e HF (nnae1r1Koeafl), HN03 H2S04 , H3PO4 6ECKV1Cn OPOAH blE HCI, HBr, H2S CV1nbHblE (a-+1) H2 S04 , HCI, HJ, KVICnOPO,QOCO.QEP>KA~VIE (r1t1APOKC1t1Abl) HCIO4 (xnopHafl), H3B03(6opHafl) cnA5blE (a-o) HMn04 (MapraH1..4oeafl) H2Cr04 (xpoMoeafl), HF, H2S, H2S03, HN02 (a30Tlr1CTafl), HCIO (xnopHoeaT1t1CTafl) no11y'-leH1r1e <!>M3"1'-leCKMe CBOMCTBa H2+ HMe -+ Hx3f BKYc! P-pbl K1t1cnoTHbl~ + H 0 -+ H 30 (p ) >K1t1AK. TeepA. ra3oe OKCIAA 2 x Y · H2S04 ~ HCI, HBr, K1t1cn0Ta + conb -+ K1t1cn0Ta + conb HN03 H3P04 H2S, (! 11111111 f ) HCl03 H3 B03 HCN S0 + 2HN03 -+ H SO + 2NOT (c1t1H1t1I1bHafl) BOCCT. OKl1CJ1. 2 4 H20 H2C03 { KOHLI. H2S0, HNO OKl1CJ1. 3 XMMM'-leCK"1e CBOHCTBa H 30 11 ~-P H++ 30 x- cTyneH4aTo x y +- x y a.1>a.2 M e (Ao H2) -+ .Q H2 i Me -+r- H2 0 +? I-IV ~ MexOy -+ Q+ H20 OCHOBaH1t1e -+ HzO COJ1b -+ {) J. KIACilOTa Hx30Y -+ Klt1CJ10THbl~ OKCIAA + H20 16HCl- 1 + 2KMn04 -+ 2MnCl2 + 5CI~ + 2KCI + 8H20 BOCCT. P.s1A HanpH>KeHMH MeTa1111oe K Ca Na Mg Al Mn Zn Cr Fe Ni Sn Pb H2 Cu Hg Ag pt Au - yeen1t14eH1t1e BOCCTaHOBlt1TeJ1bHblX CBO~CTB - - ~aCT:b 1 Knacc1r1cp1r1Ka41r1.s1 CPE.QHV1E Mex3y Mex30y NaCl KV1CnblE (H) OCHOBHblE (OH) MexHz3y Mex(OH)z3y KHC03 MgOHCI Al2(S04) 3 NH4N03 r1t1APOKap60HaT K r1t1,QpOKcoxnop1t1,Q Mg Ca(H2P04 ) 2 Fe(OH)2N03 HVITpaT aMMOHVlfl A1t1r1t1Apo¢oc¢aT Ca A1t1r1t1APOKCOHvtTpaT Fe(lll) .QBOLliHblE KOMnn EKCHblE Me1Me230y [Cu(NH3)4 ]S04 NaCl• KCI cynbQJaT K2NaP04 TeTpaaM1t1H Cu (II) opTo¢oc¢aT Na[Al(OH)4]+:! Kafl1t1fl-HaTp1t1fl ;::! Na++[Al(OH)4 ]- <J>1r131r1yecK1r1e CBOHCTBa TsepAbre + H20 ~ pacTsop1t1Mb1, Ma.11opacTsop1t1Mbl, HepacTsopvtMbl nony'-leHMe OCHOBaH1t1e " + H20 Klt1CJ10Ta + OCHOBHble MexOy -+ .J.I + H20 MeaKT r- + H2i L11eno4b + KVICilOTHble ..., + H 0 OKC1t1Abl 0 2 Klt1CJ10Ta + KVICilOTa conb + L11e1104b I + ocHosaH1r1e ! COJ1b (p.) ,,/ + COJ1b ! Me + HMe -+ Me.3y X1r1M1r1-..ecK11te ceoMcTaa (p.) (p.) (p.) Me(aKT1t1BHee)--+ Klt1CJ10Ta Ll..leflOYb COilb (p.) - --+ Me(M.aKT)! KVICilOTa OCHOBaH1t1eJ. COI1b ~ nH2 0 H 2 0 r11Apon1.13 , • nH 2 0 (Kp1.1crannor1.1,qpar) to !Mex30Y 0 MexOy + HMexOy Me(N03)x ( to • (NH4)x3 t +2 2Fe Cl2 + Cl2 BOCCT. 2Kl-1 + Cl2 BOCCT. -+ 2Fe+3 Cl 3 0 ..... 12 + 2KCI 2KMn+70 4 +16HCI -+ 2Mn+2 Cl2 + 5Cl2 + 2KCI + 8H2 0 OKl1Cn. o 4Fe+2 s ·1 + 11 o .!.. 2Fe+303 + 8S+4 0 i BOCCT. 2 o 2 2 2 N'3 H NO .!. N° i + 2H 04 2 2 2 rMAPOTIM3 Pa311o>KeH1t1e con1r1 BOAO~ c 06pa3osaH1t1eM cna6oro 311eKTpon1t1Ta. 1 .--- CQflb ~l Clt1J1bH. Klt1CilOTa cna6. 0CHOBaH1t1e r1t1Apon1113 no KaT1t10HY K"• Kn++HOH -~ KOH(n-1 )++H+ cna6. cpe,qa 3neKTpon1.1r K1<1cnaS1 Clt1J1bHOe OCHOBaHvte cna6. KVICilOTa r1t1APOI11t13 no aHVIOHY An- An-+H+OH+:!HA(n+1 )-+0H- cna6. cpe,qa 3neKTpon1.1r L11enoYHaSl cna6. 0CHOBaH1t1e cna6. KVICilOTa no Kn+IA An- K"++A""+H+OH"+:!KOH(n-1 )++HA(n+1 )- cna6b1e 311eKTpo1111rb1 cpe,qa HeiilrpanbHaSl rvtApOI11t13 yc1t1J11t1Ba10T A06asneHlt19M BOAbl, HarpesaHlt19M CIACTeMbl ..
NaOH. KOH, NH;.OH Ca(OH)2' Cu(OH)2' Al(OH)3 <l>M3Ml.feCKMe CBOHCTBa TaepAble OCHOBaHll15l non~eHMe -+ ~eno4b + H2l ~eJl04b HEPi-C~BOPv r~ b E Cu(OH)2, Fe(OH)2, Fe(OH)3 PACTBOP~MblE (~enoY 111 ) LiOH, KOH, Ba(OH)2, Ca(OH)2 + H20 ~ 3J19KTPOJ11113 BOAHblX paCTBOpos conei:i ~eJ104HblX Me 2NaCI + 2H20 1. Cl2 + H2 + 2NaOH ~0110Yb CV1JlbHblE (a-+1) ~e1104111 CJ1A5blE (a-+O) HepacTsop111Mb1e, NH40H XMMM"'leCK"'1e CBOMCTBa Me(OH)x KlllCJlOTa v KlllCJlOTHbllll OKClllA COJlb (p.) eAK111e pacTaopb1 L11e1104e~ COJlb (p.) + ~eJ104b -+ COJlb + OCHOBaH111ei Me(OH)2 + 2HCI OCH.CB-Ba Me(OH)2 + 2H+ AMQ>oTepHble rMAPOKCMAbl Mef O f H + 1- 0 + H M 2+ 20H- H : : OH- 2H+ M 0 2 - [M (OH) ]2 -e + . .....................=: ~---··-····--·:• + e eB KlllCilOlll B l!.leflOYHOlll 2 4 cpe.Qe cpe,ae -+ MeCl2 + 2H2 0 -+ Me2 + + 2H 02 • Me(OH)2+ 2NaOH Kl1C!l. CB-Ba 2NaOH + Cl~ -+ Nacr 1 + NaCl+ 1 0 + H20 -+ Na2Me02 + 2H2 0 TOYHee: -+ Meo 2 - + 2H o Me(OH)2 + 2NaOH -+ Na2 [Me 2 +(0H)4 ] 2 Kll!Cfl. CB-Ba OKHCJ1. BOCCT. Me(OH)2 + 20H. 2 2 Me(OH)2+ 20H- -+ [Me(OH)4 ] 2 - 1887 r. CaaHre AppeHvtyc //1. A. Ka6nyKoa np111 paCTBOpeHll1111 B BOA9 (11111111 pacn11aa11eHL-1111) 3J19KTpOJ1111Tbl pacnaAalOTC5l Ha nono>K111TeJlbHO 111 0Tp1111..1aTeJlbHO 3ap5l>KeHHb1e 1110Hb1 (nOABepralOTC5l aneKTpo11111T111- 4ecKo~ A111cco1..1111a1..1111111). KOHf..19HTpaf..11115l 1110HOB B paCTBOpax 3aBll1CL-1T OT Toro, HaCKOJlbKO nOJlHO AaHHbl~ aneKTpo11111T Alllcco1..1111111pyeT Ha 1110Hb1. HE3J1EKTPOJ11f1Tbl: 3J1EKTPOJ11f1Tbl: 60JlbWlllHCTBO opraHll149CKll1X B9U9CTB, H9M9T8J1Jlbl, M9TaJ1Jlbl Kll1CJ10Tbl, OCHOBaHll15l, COJllll (npoBOA5lT 311. TOK B pacTaopax, pacnnasax) Et) -+ KaTOA- 8 -+ 8HOA + CreneHb ,[lMCC04vta4vtvt (a) - OTHOWeH111e 4111CJ1a pacnaBWll1XC5l Ha 1110Hbl MOJleKyn (n) K 06L11eMy 4111CJ1Y paCTBOpeHHblX MOJleKyn (N): na = - NL-1 Bb1pa>KaeTC5l s AOJ15lX ep.111Hll1'-1bl 11111111 a npo1..1eHTax (a<0,03 - cna6b1e; 0,03<a<0,3 - cpep.H111e; a>0,3 - c11111bHb1e aneKTpo11111Tb1). CTeneHb p.111cco1..1111a1..1111111 3aa111c111T OT np111pOAbl aellleCTBa, KOH'-1eHTpa1..1111111 pacTaopa, A06aaneH1115l 1110Hoa. KoHCT8HTa ,[lMCC04vta4vtvt (KAlllC) - OTHOWeH111e npOV13Bep.eHll15l paBHOBeCHblX KOHf..leHTpal_VI~ 1110HOB 8 CTeneHll1 COOTB9TCTBYIOU111X CTeXll10M9TPV1- 4eCKV1X Koacpcp1111..1111eHTOB K KOHf..1eHTpa1..1111111 H9A111CCOf..1111111poaaHHblX MOJleKyJl. _ [K+][A] . K.Q"1C.- [AK] • BOAOPOAHblM noKa3aTenb pH=-1g[H+] [H+]=[OH-] Hei:1TpanbHa5l pH=7 [H+]>[OH-] KV1CJ1a5l pH<7 [H+]<[OH-] Uell04Ha5l pH>7 oo- o+Z> o+ H 1os0 H rMAPOKCMAbl KvtCJlOTbl 0CHOB8HVl5l ~ ,QVlnOJlb Hx30y +-+ H+ + H30y II H30y +-+ H+ + 30y- Hx30y +-+ xH++ 30y- Me(OH)x +-+ [MeOH]++OH- 11 MeOH+ ..... Mex+ +OH- Me(OH)x +-+ Mex+ + xOH- cx.,>CX.11 AMcpoTepHble Mef Of H 1- 0 + H + - K = [H ][OH ] K = [H+][OH-]=1 o-14 Al-IC. [H20 ] ~ H~ MexaHM3M 3neKTponMTM"'leCKOM AMCco4"'1a4MM a pacnnase + + ltlOHbl 0 ··+t Kl!ICJlble I Me(H3) ..... Me++ H32- ll H3 2 -..... H++ 32 • ConM OcHoBHb1e [MeOH]3 ..... MeOH++ 3 · 11 MeOH+ ..... Me2 ++OH- Me(H3) +-+ Me++H++ 32 • Me0H3 - Me2++OH-+ 3 - CX.1 ~ex.II Cpe.qHvte Mex3y +-+ xMey++ y3x- + ' ' OH- Me2++ 20H-~-----tt____:J L--------·--·:+ 2H++Meo2 · [Me(OH) ]2 - s KlllC!lOlll B L!.19JlOYHOlll 2 4 cpe.ae cpe,ae H+ Li+ NH4+ K+ Na+ Ag+Ba2+Ca2+Mg2+zn2+Mn2 ' Cu2 • cu+ OH- p p p p - p H H H H H NOi p p p p p p p p p p p p p F- p p p p p p H H H - c1- p p p p p H p p p p p p p Br - p p p p p H p p p p p p - ,- p p p p p H p p p p p - - S£ p p p p p H - - - H H H - so~· p p p p p H - H so~· p p p p p H p p p p p co~· p p p p p H H - H H - - SiO~· H - - p p H H H H H - - Po:· p H p p p H H H H H H H H cro~· p p p p p H H ,, p H H H - CH3COO- p p p p p p p p p p p p p Hg• Hg2+ Pb2+Fe2+ Fe3+ Al3+ - - H H H H p p p p p p H H p p H p p p p H '1 ~ p p p H - H p p p H H H H H - H - H - - lP p H p p p H H H H H - - - H H - - H H H H H H - - H - - - p p p p p p Cr3+ 8j3+Sn2+ H H H p p - p H p p - p p - p - - - H H - H H p p p - H - - H - H H H - H - p p p Sr2 • p p p p p H H H H H ~ p p M H - - pacTsop111Mb1e (> 1Or s 1000 r H20) - ManopaCTBOpVIMble (OT 10 .qo 0,01 r B 1000 r H20 ) - HepacTaop111Mb1e (< 0,01 r s 1000 r H20 ) v - pa311ara10TC5l aop.0111 11111vi He cyllleCTBYIOT MHcjJopMa4110HHo-cnpaao~HaR ra6n114a © 000 «MHcjJonnacr", 2004 r. MocKaa, Kaw11pcKoe wocce, 21 E-mail: mail@infoplast ru Http:llwww.infoplast ru Ten.: (095) 320-94-89 <1JaKc: (095) 320-94-88 no,qnucaHo a ne~arb 25.08.05. T11pa>1< 40003K3. 3aKa3 N92103. "13,qarenb 000 «MHcf>onnacr", MocKaa, Kaw11pcxoe wocce, 21. TunorparjJ11R 000 «Busa-Crap». 107023, MocKaa. yn. 3neKrpo3aao,qcKaR, 20 ..
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Ha nOAYPOBHe: ***gi~~HH~ee n=1 , :=0, Ha ypoeHe ··· 1s ·· op61o1rnnb (:) 2. np11H411n naynw B Ka)f(AOi.1 aTOMHOi.1 op611rnn11 MO)f(9T pa3- Mell.laTbC5l MaKCl1ManbHO ABB aneKTPOHa. 3. npaa11no XyHp,a: mmm .'-- ' t • • I a -pacna,o, n=2, :=1 , Ha ypoeHe ···2s+2p ···(:::) op61>1Tan1o1 n=3, :=2, Ha ypoeHe ··· 3s+3p+3d (V) op61>1Tanei.1 MBKCl1ManbHbli.1 cn11H aTOMa: ITIIIIl ~ ••• ••• neplllOAlll"leCKa~ ClllCTeMa Xl.1Mlll"leCKlllX 3fleMeHTOB ,Q. Ill. MeHAeneeea 1829 r. , Ao6epeillep - BblAemm TP11aAbl 3neMeHTOB. 1864 r., Meillep - 06b9A11Hl1n 3neMeHTbl B COOTB9TCTBl111 c X11MW-19CKl1Ml1 CBOi.1CTBaMl1. 1865 r., Hbl0fl9HP,C - TeOpl15l OKTaB. CoepeMeHH&fl ci>opMyn11poeKa nepMOAMYeCKoro 38KOH8. 1869 r., MeHp,eneea - B ocHoee aTOMHa5l Macca. nep11op,114eCKl1H 3BKOH: CBOi.iCTBa npOCTblX Ten, a TalOKe CBOi.iCTBa C09A11H9Hl1i.1 3neMeHTOB Ha- XOA5lTC5l B nep110A1149CKOi.1 3aBl1Cl1MOCTl1 OT aTOMHblX B9COB 3neMeHTOB. Ceoi.icTea x11M11YecK11x aneMeHTOB, a TalOKe CBOi.iCTBa C09Al>IH9Hl1i.1 o6pa30BaHHblX 3Tl1Ml1 ane- M9HTaMl1, HaXOA5lTC5l B nep110A1>149CKOi.1 3aBl>tCl>t- MOCTl1 OT 3ap5lAOB aTOMOB. ] g:,.Cl. "c: Ill H LI mm11il ~ 6.941 Na I "" HBTpMM ~ 22.99 K R,0 11 19 rpynnbl3neMeHTOB Ill IV V VI VII RO R20 , RH4 R02 RH, R20 5 RH2 RO, RH R20 7 Be 6epMJmMM ; 9.0122 4 B 6op = 10.811 5 c N yrnepoA 830T ~ 12.011 ~ 14.007 0 KMCllOPOA ~ 15.999 Mg 12 Al 13 Si 14 P 15 s 16 1 M8rtu1M t 24.32 2 aJ110MMHi.1~ l 26.092 21 l KpeMHM'1 ' ¢>oc¢iop ~ 28.086 : 30.974 5 cepa i 32.064 Sc 22 Tl 23 v 24 F ¢oT0p- ~ 18.998 Cl e Xl10p I 35.453 17 Cr 25 Mn VIII R04 28 Ni IV ! KBnMM 39.102 : ~ .., , CK8H,Qlll~ ~o 44.956 I TlllT8H ~1 47.956 : BBHSAlllM ~2 50.941 : xpoM ~3 51 .996 : Mapratte1...1 54.938 26 Felf, >Keneao ~e : 55.848 : 21 Co'IK068TlbT ~8 58.933 : H.1K0Ilb 58.7 v .'."' .K 2 29 Cu M0,Qb ~I 63.546 : 30 Zn Ga Ll.1HK fanJ1.1M 65.37 69.72 31 Ge ,: repMaH1o1M : 72.59 32 As 1: MblWbSlK : 74.922 33 Se 1~ ce.neH I 78.96 34 Br ,: 6pOM I 19.904 35 ' ".' , 44 Ru1 I'45 ;: pyreHM~ :: ~ 101 .07 2 Y l:'• 40 Zr 1:,''2 41 Nb , 42 Mo ~3 43 Tc ITTTpHM l.1"1PKOHlllH HH06111M i: MOI11116AeH 1e T0XH01.1HH 88.906 a 91.22 92.906 a 95.94 I (99] Rh:1· 46 Pdpo,QMH i: nannSAlllH 0 Rb 31,Sr 38 ,,39 VI : ~M ,: CTJ>OHL4MH ,: ~. ~ RS.468 I e1.62 : I 102.906 a 106.4 530 , 47 Ag l,., 48 Cd In VII : ~= cepe6po Ka,QMlllH lo1H,qlo1&11 49 ~1, !~BO 50 ~!, !~bMa 51 :!, ~~nyp 52 ~1, ~OA ' ""~ : 107.868 : 112.41 114.82 118.69 121.75 127.6 126.905 l VIII 0 ··.', CsLl93MM 132905 55 : "·:. Ba 15apMli 137.34 ix ~~ ~::: 19 Au h80 ~:.:~ i' x 0 0:' Fr 87 ' =·=.· CIJpaHl.IMM i [2231 Ra Pai:l<ii (226) 57-71 La-Lu fl8HTSHOHAbl !~ 12 Hf ;:,:• 13 Ta ~2 14 W ~:',', 15 Re k,·, 1s •," ra¢>H1o1H T8HTan ~ eonbtj:lpaM peHlllM 11a.49 180.948 I 183.85 186.201 i Os ll, 11 Ir I:, 78 Pt OCMlllH ~ lllPM.QlllH ~ nnaT111Ha 100.2 I 192.22 : 195.09 Hg Tl s1 h,::, Pb 82 h,:, Bi 83 h,',s Po 84 1: At PTYTb rann111M ce111Het.1 e111cMyr nonott111M tl acrar 200.s9 204_31 201.19 : 208.98 I [2101 I [2101 88 J..".. 89-103 Ac-(Lr) ""'""""'"" il 104 R! !~ 105 Db ~ 10& Sg h101 11 peaep¢op.QMM ~: AY6H1o1M ~: CM6op1111M ~: I 12611 : (2021 : l263J I 85 1~ ll l Bh ~ 108 Hs lh109 Mt:lh110 Os 6op1o1H ~ xaccHK U MeKTHep111'1 ~: ,ciapMcra,r:rrnYM [262] : [265] : {266] ~ [269] Ha renMM 4.003 Ne H80H 20.179 Ar aproH 39.948 Kr t<p.1nTOH 83.8 Xe KeeHOH 131.3 Rn PCIAOH (222) 10 18 36 ."l 54 :! l 86 ~ I 57 la : sa Ce : 59 Pr I 60 Nd i: fl8HT8H l: 1.1ep111K U~MM ~ H80AlllM I 63 Eu : 64 Gd ~ 65 T~ L66 D)'. L67 H~ L68 E~ !,&9 T~ L10 Y~ !, 11 L~ ~ eepomtK ~ ra.QOJ1MHMl°1 11 rep6111o1 11 ,ci111cnpo3HH 11 ronbMllllll ,, ap6111111 11 ryn 1o1111 11 ITTTep6Hvi ,, more1.11111o1 : 138.906 : 140.12 : 140.908 2 144.24 : 151 .00 : 1s1.2s : 1sa.e26 i i s2.s : 164.93 l 161.20 : 1ss.e34 l 113.04 : 114.97 I u Ac :, 90 Th I 91 Pa I 92 U I 93 Np l 94 Pu l 95 Am l 96 Cm I 97 Bk l 98 Cf I 99 Es l 100 Fm I 101 Md l 102 No : 103 Lr r. SKTMHMM r. TopMM HnpoTalm!MMM ~ ypaH ft HBITTyHMH ennyroHMl4 ~ aMepH~M ~ KtOpMM ft 6epKnMM ft~lllK aMtwreMHMM e¢>epMMM i M8HASn&BMM ~ Ho6e.nMM ~ noypeHCMM : (227] : 232.038 : (231} : 238.29 : (237) : [244] : [243} : [247] : [247] : (251) : [254] : [257] : (258] : [259] : [260] B nep1110,qe: B rpynne: ,Q. Ill. MeHAeneee 1834 - 1907 rr. nop$1AKOB9fi'il HOMep ClllMBOO aneM0HTa 25 Mn ~2 MapraH0LI ; 54.938 Onioc111renbH8$1 aTOMHasl Macca Pacnpe,QeneHHe aneKTpoHOB no CJlOSIM D s - 3neMeHTbl D p -3J19M6HTbl D d -3110M6HTbl rn f - 3fleMeHTI:.I HoMep 3neMeHTa: 3aP"'A flApa, cyMMapHoe 41>1Cfl0 aneKTPOHOB, 411Cno npOTOHOB. HoMep nep1110,qa: Y1>1cno 3HeprernYeCK"1X yposHeii. Mei - MeTanna.1YecK11e caoiicrna YMSHbWatoTCfl; Met - MeTann11YecK11e caoiicrna yeena.1Y11sat0Tc5l; HoMep rpynnb1: 41-!cno saneHTHblX aneKTpOHOB, MaKC"1ManbHYIO nonO)f("1T9nbHYIO CTeneHb OK"1CneH"15l (CO) 3ap51A "'APa ysen11Y1>1saeTcfl; paA11yc aTOMa yMeHbwaeTcfl; •mcno BH9WH"1X aneKTPOHOB ysen"1411BaeTCfl; npOYHee 11X CBfl3b c "'APOM. sapflA "'APa ysen1>1Ya.1saeTcfl; paA"1YC aTOMa yysenH4"1BaeTCfl; 4"1Cno BH9WH"1X aneKTpOHOB noCTOflHHO; cna6ee 11X CBS'l3b c "'APOM.
3ro ~ AfJyx aTOMOB, ocy114ecTem1eMoe nyre M o6MeHa 3neKTpoHaM11. ()()pa3oeattMe ~Koiii CBSl3M - OObeAHH0Hl10 aTOMOB B Monet<ynbl. X11Ml140CKaSI CBSl3b - Q:>opMa Bb111rpblwa 3Hepf"Ml1 ~ npM 00pa3088Hl111 XMMM40CKOM CBSl3M aTOMbl CTp0MSITCSI np1106pecrn YCTOM411BYIO BOCbMl13fl0KTpoHHYIO (11n11 AByx3neKTpoH- ~ HYIO) BHeWHIOIO o6on04t<y, COOTB0TCTBYIOU4YIO CTP00Hl1IO aTOMa 6n11:>Kai1Ujero 11H0pTHOro ra3a (npae11no OKTeTa). Pa3nM48IOT Cfl9AYIOU4119 B11Abl Xl1Ml140CKOM CBSl311 : KOaaneHTHaR (nonSlpHaSI 11 HenonS1pHaS1; o6MeHH8SI 11 AOHOPH0-8K4enTOPH8SI), HOHHaJI, ao,qo- p<J,qHaJ/ 111.1erannw-1ecKaJ1. lilOHbl - 3TO 3apSl:>K0HHble 4aCTl14bl, B KOTOpb1e npeepa114a10TCSI aTOMbl B pe- 3ynbTaTe OTAa411 11n11 npl1C00A11H0Hl1SI 3neKTpOHOB. llTOHHaR CBR3b - npeA0flbHbllil cny- 4ai1 KOBaneHTHOi'! nonS1pHoi1 CBR311. KoaaneHTHOCTb - 411cno 0611411x 3fl9KTPOHHblX nap. 3neKrpoorpu4arenbHOCTb (30) - cnoco6HocTb aToMa np11TS1r11eaTb CB060AHbl0 3fl0KTpOHbl (wKana n. no- n11Hra). 30 eo3pacrneT s nep110Ae. yMeHbwaeTCSI s rpyn ne. nep110A 30T lj N~°F(4,1) e- 30! Sc (0,86) Br X11Ml140CKaSI CBSl3b M0:>KAY 110HaMl1, ocy114ecTBnS1eMaS1 3a c4eT aneKTpocTa- Tl149CKoro npl1TSl:>K0Hl1SI , Ha3blBaeTCSI MOHHOM CBSl3bl0. 1916 r., 11A0SI KoccenSI K· + :;: ---+ K+ [:~: f 1,11 vi,v11 lllOHbl nepeXOA ne Na.+.~1:--+ Na+[:~1:r I I C111nb1 - (±)-0- np111H1>KeH111s:i --+_Ji-~- 1 I VIKP cpi1131114eCKllle CB-Ba: T T~n.l H20 p-p, pacnnaB 7 Ecn11 pa3HOCTb 3neKTpooTp114a- TenbHOCTei1 aTOMOB een11Ka, TO 3fl9K- TPOHHaSI napa, ocylljeCTBflRI01l4aS1 CBSl3b, nepeXOA11T K OAHOMY 113 aTOMOB, 11 o6a BaneHTHb1e 3neKTPOHbl MeTannoe AOCTaT04HO cna6o CBSl3aHbl co CBOMMM S1APaM11 11 MOryT nerKO OTpblBaTbCSI OT H11x. no3TOMY Mernnn c0Aep:>t<11r PSIA no- no:>t<11TenbHb1x 110HOB, pacnono:>KeHHblX B onpeAeneHHblX nono:>KeH11S1x Kp11cTann11- 4ecKoi1 peweTK11, 11 6onbwoe KOnl149CT- eo 3fl9KTpoHOB, CB060AHO nepeMeuta10- 1l411XCSI no BCeMy Kp"1CTanny. 3neKTpOHbl B Mernnne ocylljecTsnsi- IOT CBSl3b M0:>KAY BC0M"1 aTOMaMl1 MBTan- na. Me0 - ne --+Me"+ Me"++ ne --+ Me0 Cl>113M4 0CKMe CBOMCTB8 T (Hg - >K) 7 rnnno 6necK' KOBKOCTb Ocylljecrsns:iercS1 3a c4eT 3neKrpOHHOlil napb1, n p11H~e:>Kalljei1 o6o"1M aToMaM. Ecn11 aneKTPOHHaSI nnoTHOCTb pacnono:>t<eHa C"1 MM9Tpl14HO M0 :>KAY aTOMaM"1 , KOBaneHTHaSI CBR3b Ha3blBaeTCSI HenonsipHOM. Ecn"1 3neKrpo HHaS1 nnoTHOCTb cMe114eHa B CTOpoHy OAHOro 113 aTOMOB, TO KOBaneHTHaSI CBSl3b Ha3blBaeTCSI no11S1pHOM. HenonsipHasi: 30=30 no11S1pHaS1: 30> 30 Pa3n 114a10T o6 MeHHbli1 11 AOHOpHo- aK4enrop- Hbli1 Mexa H"13M o6pa30BaH"1SI KOBaneHTHOi1 CBSl311. 06MeHHb/H MexaHH3M Ka:>KAbli'I aTOM Aaer no OAHOMY HecnapeHHOMY 3fl0KTPOHY B 06Ujyl0 3neKTpOHHYIO napy: A-+ ·A-+ Ar;:;iA A·+ ·B--+ Ar;:;iB :r. + ·r: --+ :r : r: .. a·· .. •• --(XIX)- r-r :6 . + ·6:--+ :6 :: 6 : '* O=O " I I MKP -@- @- ~---+ I I :r: - @-@- ~ I I g:---+ <±3 <±3 ~ <±3 c .. ..H· +· r:--+H: r :a •• •• --o:::x::>- H-+H Cl>M31140CKl19 CBOMCTB8 T, >K, r T~.! H20? neTyY111e Ji I I AKP ~ -®-®- !::......< ()---+ I I CT T~n.l ~ -®-®- I I Cn, Sin, (Si02)n. SiC ,qoHOpHo-aK4enropH&1if MexaHH3M 0A11H aTOM (AOHOp) npeAOCTaBnSleT 3fl9K- Tp0HHYIO napy, a APYrolil arnM (aK4enrnp) npeAO- CTBn S1eT AflR 3TOi1 napbl CB060AHYIO op611Tanb: Ao7op A: +oB+--+ Ar;:;iB+ '--' I aK1..1emop NH +H+--+ [ ~ ]+li10H ·~ 01 H"~'H aMMOHli1s:l s H :QH .. "! .. HO:-+Al3 .+--:0H KOMnneKCHblM li10H (TeTparli1APOKCO- anIOMHaTaHli10H) l :OH BOAOPOAH8SI CBSl3b 3 TO CBSl3b M0:>KAY nonO:>K11TeflbHO 3apS1:>K0H- HblM aTOMOM BOAOPOAa OAHOi1 MOfl0KYflbl 11 OTp11- 4aTenbHO 3apS1:>t<eHHblM aroMOM APYroi1 Monet<y- nb1. BOAOPOAHas:i CBR3b "1Meer 4acrn4HO 3neKTpo- crnrn4ecK"1i1, 4acrn4HO AOHOpHo-aK4enropHbli1 xa- paKr ep. 8- 8 + Bo,qopo,qHafl CBR3b vt3o6paJKeHa TO'!KBMM H--+3 .. . H---+3 ..8- H--+ O: ... °"'H 8 + .. H --+O: °"'H PeaK4HH HOHHOro o6MeHa PeaK4uu pa3noJKeHvtR - peaK41111, e pe- 3ynbTaTe KOTOpblX "13 OAHOro BelljeCTBa o6- pa3ylOTCSI ABa 11n"1 HecKonbKO APYrHX ee- UjeGTB. 2CH4 _!; C 2H2t + 3H2t PeaK4uu coe11uHeHvtR - peaK41111, B pe- 3ynbTaTe KOTOpblX 113 ABYX 11n11 H0CKOflbKl1X ee114eCTB 06pa3yeTCSI OAHO HOBOe B9Uj9CTBO. 2Fe + 3Cl2 ...... 2FeCl3 PeaK4uu 3aMe1.14eHvtR - peaK4"111, npore- Kal0Ujl1e MB>KAY npoCTblM"1 "' cno:>KHblM"1 ee- Uj0CTBaM"1; np11 KOTOpblX aTOMbl npOCTOrO ee- Uj9CTBa 3aMelljalOT aTOMbl OAHOro "13 3ne- M9HTOB B CflQ)l(HOM B8Uj0CTBe. 2AgN03 + Fe ...... Fe(N03)2 + 2Ag ! PeaK4uu o6MeHa - peaK41111, npoTeKa10- Uj11e MB:>KAY ABYMR cno:>t<HblMl1 BelljecreaM11, np11 KOTOpblX "1X COCTaBHble 4acrn o6MeH"1Ba- IOTCSI MeCTaMl1. Fe2(S04)3 + 3BaCl2 ...... 3BaS04i + 2FeCl3 OKHCnHren&Ho-soccraHoBHTen&H&1e peaK4HH PeaK14vtvt pa3noJKeHvtR OKHt m'IT9 11b 10 2Hg0 ...... 2Hg + 02t BOCCT8HOBHT911b PeaK4uu coe1JvtHeHvtR 4Li + 0 2 ...... 2Li20 PeaK4Hu 3aMe1.14eHvtR Zn+ 2HCI ...... ZnCl2 + H2t TepMOXHMH'lecKHe peaK4HH 3K3orepMvt4ecKue - peaK4"111, npoTeKa- 10Uj11e c Bb1A0fl9 Hl10M rennOTbl. H2 + Cl2 =2HCI + 184,6 KA>K 3HIJOTBpMvt4eCKvte - peaK411"1, npoTeKa- IOUj110 c nornOUj0H"10M TennOTbl. 1 1 2 N2 + 202 = NO - 90,4 l<A>K Tennosoilr 3cfJ<jJBKT XVIMW-leCKOH peaK4vtvt 3TO KOfll140CTBO TennOTbl, Bb1A0flSllOUjei1cSI B pe3ynbTare peaK41111 . 06paTHMble H Heo6paTHM&le peaK4HH Heo6parvtMb1e peaK4uu - peaK41111, npo- TeKalOUjl1e AO KOH4a, T. e. AO nonHoro "13pac- XOAOBaH"1SI OAHOro 113 pearnpyl0Ujl1X ee- UjBCTB. Ag+ Cl -+ AgCI 06parvtMble peaK4uu - x11M"14BCK"1e pe- aK41111, nporeKalOUj"1e np11 AaHHblX ycno011S1x eo B3al1MHO nporneonono>KHblX HanpasneH11- S1X. V1HcjJOpMa4HOHHO-Cnpaao,HaR ra6nH4a ©000 «MH<Ponnacr., 2004 r. MocKaa, KaumpcKoe wocce, 21 E-mait mail@infop/ast ru Http:llwww.infop/astru Ten.: (095) 320-94-89 <PSKC: (095) 320- 94-88 not{m1C8HO B nelf8Tb 26.02.07. TMpa:« 4000 3K3. 3aK83 Ng 3497. "13,lfBTeflb 000 «MHcfJOnnBCT•, MOCKBB, KawMpCKOB WOCCe, 21. T111norp8c/JMR 000 «Bvtaa-Crap». 107023, MOCKBB, yn. 3neKTp038BOACKBR, 20.
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HanpVIMep, VIHAeKCbl B cpopMyJle rVIApa3VIHa N2H4 noKa3blBalOT, YTO e MOJleKyne rV1Apa3V1Ha Ha 2 aTOMa a3oTa npVIXOAVITC51 4 aTOMa BOAOPOAa, a B 1 MOJlb MOJleKyfl rVIApa3VIHa Ha 2 MOflb aTOMOB a30Ta npVIXOAVITC51 4 MOJlb aTOMOB BOAOPOAa. 3aKOHbl CTeXMOMeTpMM. 3TOT 3aKOH OTKpblT VI 3KCnep111MeHTaJlbHO o6ocHoeaH M.B.noM0Hocoeb1M (1748), a 3aTeM cppaHU,Y3CKVIM XVIMVIKOM A.naeya3be (1789). 3TOT 3aKOH rnaCVIT: .- nocne OTKpblTVl51 A.3HWTeiliHOM B 1905 r. B3aVIMOCB513VI Me>KAY Maccoili VI 3Heprvieili, KOTOpa51 BblpaJKaeTC51 ypaBHeHVleM E=mc2 rAe E-<1HeprV15I; m-Macca; c-cKopocTb ceera e eaKyyMe, 6b1Jl ccpopMyllVIPOBaH 6onee 06°Ll.!Vlili
0THOWeH"1e M cc K"1CnopoAa"' 330Ta B OKC"1A3X'a30ilia. 0KCHAa30Ta N20 NO N203 N204 N205 3aKOH <t>opMy11111pyeTCR o6pa30M: CyMMa Maccbl seutecTsa CHCTeMbl ,,, MaCCbl, KOTOpafl 3KBHBaneHTHB 3HeprHH, nOR}"leHHOH HnH OT,QBHHOH TOH JICe CHCTeMOH, nOCTOflHHa. 3TOT 38KOH 6bl11 ycTaHos11eH A>K. AanbTOHOM e 1803 r. ECJIH ABB 3/leMeHTa 06pa3y10T Me)l(,O,y co6oii 6onee op,Horo COeP.HHeHHfl, TO MaCCtJ QQHOro 3neMeHTa, npHXOP.flutHeCSI Ha OP.HY H TY JKe Macey p,pyroro 3/leMeHTa OTHOCflTCfl Me)l(,O,y co6oif KaK He6onbWHe Lie/Ible 'IHcna. AeiAcTe111e :noro 38KOH8 MO>KHO npo111111110CTPMPOB8Tb H8 rtpM~ OKCMAOB 830T8. 3TOT 38KOH c<t>opMy11111posan B 1808 r. )I(. npycT. Ka)l(,O,oe XHMH'l8CK08 He3aBHCMMO OT cnoco6a ero non}"leH/lffl COCTOHT H3 OIJ.HHX H Tex JIC8 3J18MeHTOB, npwleM OTHOIUeHWI Hx Mace nocTOJtHHbl, a OTHOCMT8RttHt.16 KOJlH'leCTBa HX BTOMOB BblpaJICS/OTCSI l.f6/lblMH 'IHCJIBMH. 38KOHbl AaJibTOH8 111 npyCT8 cnpaB9,D,11111Bbl TOl1bKO A/lSI >KMAKMX .., ra3006pa3HblX CC>eAlllHeHMM c ra3006pa3HOM CTPYKTYPOM (Hanp!>1Mep, S02. S03, NH3, C5H5). TaKMe coeA111HeH111R e naMRTb A>K. Aa11bTOHa Ha3B8Hbl A8l1bTOH111AaM111. HapRAY c A8l1bTOHlllA8Mlll cyU.(eCTBYIOT HeCTeXlllOMeTpMYeCKllle C08AlllHeHMR- 6epTOl1111Abl. 6epTOm'IAbl-KPlllCTann111YecK111e <t>a3bl nepeMeHHOro COCT8B8, B KOTOPblX OTHOW8HlllR KOl1111Y8CTB p83HOPOAHblX 8TOMOB He MOryT 6b1Tb TOYHO Bblpa>KeHbl M8l1blMlll ue11blMlll YlllCl18Mlll. Crnx1110MeTp111yecK111e lllHAeKCbl e <t>opMy11ax 6epTOl1l1111AOB MOryT 6b1Tb Heue110YMCl1eHHblMM. 6epTOl1l1111Abl Y8CTO BCTpeYSIOTCR Cp&AM &ttt8pHblX CQeAMHeHMM Macca KHcnopoAa, npHXOAS1~aS1CS1 Ha 1 r a3oTa (1·16): (2· 14) =0,5714 (1·16): (1·14) =1,1428 (3•16): (2·14) =1,7143 (4·16): (2·14) =2,2857 (5·16): (2·14) =2,8571 cy11b<t>11tAOB T.n .) MaCCbl pearnpylOUIHX se11.1eCTB OTHOCflTCfl Me)l(,O,y co6oif KBK MOllflPHble MaCCbl HX 3KBHB8/leHTOB. 3KBlllB8neHT - 3TO peanbHQR 11111111 YCl10BH8SI eAlllHlllU8 BeU.(eCTBa, KOTOpaR B A8HHOM K111Cl10THO OCHOBHOl-1 peaKUllllll 3KBMB8neHTH8 OAHOMY K8TlllOHY BOAOPOA8 111n111 B A8HHOM OKlllCl1111T8l1bHO-BOCCT8HOBMT0l1bHOM peaKUllllll OAHOMY 3l1eKTPOHy. ct>aKTOp 3KBlllB8l10HTHOCTll1 YMCno, 0603H8Y8IOU.(ee, K8K8R AOl1R pea11bHOM YacT111~ eeU.(ecTea 3Ks111saneHTHa OAHOMY K8TlllOHY BOAOPOA8 B A8HHOl.1 K111Cl10THO- OCHOBHOM peaKUllllll 11111111 OAHOMY 3l1eKTpOHY B A8HHOM OKlllCl1111Tel1bHO-BOCCT8HOBlllTel1b- peaKU111111 . 3TO 6eapaaMepHasi B K111cnoTHo-ocHoBHOlii peaKu111111 Me>K,D,y cepOBOAOPOAOM .., rMAPOKClllAOM H8TPlllR, B3RTOM B 11136blTKe, H2S + 2NaOH = Na2S + 2H20 yYacTeyioT o6a KaTMOHa BOAOPOAa Ka>K,D,oi:.1 Mo11eKY11bl ceposoAOPOAa. B 3TOM Cl1yYae OAHOMY KQTl/IOHY w 3KBMBBn0HTHa yc11oeHaR YaCTMUa-1/2 Mo11eKynbl H2S, a faKe (H2S) = 1/2. Ec11111 >Ke cepoeOAOpoA 111 rlllAPOKClllA HSTPMR B3RTbl B T8KlllX COOTHOWeHMRX, YTO B P83Yl1bT8Te peaKUlllM o6paayeTCR r11tAPO- cy11b<t>aT H8TPMR H2S + NaOH = NaHS + H20 TO B K8)1(,ll,OH MOl1eKYl1e cepOBOAOPOA8 38M0U.80TCR TOl1bKO OAlllH K8TMOH BOAOPOAQ. B 3TOM c11yYae OAHOMY 1110Hy W 3KBMBaneHTH8 peal1bH8R MOn0KYJ18 H2S Ill f3 Ke (H2S) = 1 . Yacrnua- Ko111i1yecTeo 3Ke111ea11eHTa M3MepsieTCR e MOl1RX, KBK.., l1I06oe KOl1MY0CTBO B0U.0CTB8. Macca 1 MOl1b 3Ke111eaneHTa , r.e. MonRpHaR Macca 3KBlllB8n8HT8, paeHa npo113BeAeHMIO 0THOW9HHe Mace KHCnopoAa,npHXOASl~HXCSI Ha 1 r a3oTa, K0,5714 (Toit'JKe senH'IHHe .ctnR N20) 1 2 3 4 5 <t>aKTOpa 3KBMB8n8HTHOCTM Ha MOl1RPHYIO Macey seU.(ecTBa. Hanp111Mep, MOl1RpHaR Macca 3KB111ea11eHTa cepoBOAOPOAa B KMCl10THO-OCHOBHOM peaKUMM c M36blTKOM rMAPOKCMAa H8TpMR M(1/2 H2S)= a f3Ke (H2S) ·M(H2S) B paBHblX o6beMax pa3/IH'IHblX ra30B npH OP,HHaKOBblX TeMnepaT}'pax "' .o.asneHHH co.o.ep)l(HTbCfl 0P,HH8KOBOe 'IHC/10 MOlleKyll. l-13 3aKoHa AsorQAPo cneAyeT, YTO: *1) np111 HOPMBnbHOM Aae11eH111111 (101,3 Kna=1 aTM) .., TeMnepaType o0 c 1 MOl1b ' mo6orc ra3a 3aHMMaeT o6'beM 22,4 n; *2) nJlOTHOCTM AByx raaoe npM OAHMX .., Tex *e A8Bl10HMM 111 TeMnepaType npRMO nponopuMOH8nbHbl MX MOl1RPHblM M8CC8M. 3TOT 38KOH 6bln OTKPblT B 1808 r. )I(, n.relii- l'lpH nocTOJtHHOM .o.asneHHH ,,, TeMneparype OIMMW pearnpy1011.1Hx Me)l(,O,y co6oif npQA)'tC108 peSKl.llAH OTHOCflTCfl KSK Het1onbWHe "811bl8 'IHC/llJ. I4607061 652306 MH<l>opM&l4MOHHO· cnpaao'IH&R Tal511M14a 000 "lllHQ>onnacr", 2006 r. MocKea, Kaw111pcKoe wocce, 21 e-mail: mail@infoplast.ru, http://www.infoplast.ru TBJI., (495) 320-94-89/88

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Шпаргалки

  • 1.
    paBeHCTBa: ao = l;am· an = am+n; am: an = am-n (amY=amn; (ab)n =anbn; (~J an a-n 1 ~ = lal ={a, ecJIH a ~ 0, -a,ecm1a <0 OcHOBHble CBOMCTBa MOAYfljt: la!~ O; lal-lbl ~ la ±bl~ !al+ lbl; I-al= la!; la-bj =lb-al. 1. Apu<jJMemu1JeCKaR. (~) (a, - nepBhIB 'IJleH, d - pa3HOCTb, n - '111CJIO 'IJieHOB, an- n-H 'IJieH, Sn - cyMMa n nepBhIX 'IJieHOB) an =a, +d(n-1); a11- I +an+Ia = . n 2 ' d a d =an - am ' (n ...,. m),·= n+I - an; ..,... n-m S = a1 +an ·n = 2a1 +d(n-1) ·n- n 2 2 ' an+am =ap+aq,rJJ,en+m=p+q. 2. I'eoMempu'leCKaR. (-:--:-) b1 - nepBhJH 'IJleH, bn - n-H 'lJieH (bn * 0), n- '!HCJlO 'IJieHOB, q- 3HaMettaTeJih ( q * 0 ), s,, - C)'MMa n nepBbIX 'IJieHOB bn=b1·qn-I; b;=bn-1.bn+I' bn*O; S __ bl (1-q") __ bl -bnq --~ IlpHq *l; n 1-q 1-q S11 =n ·b1npH q =1; q __ bn+I ,· n-m bnq =-· bn bm' b11bm =bpbq,rJJ,en+m= p+q Cy.M.Ma 6ecKoHe'lHOU zeoMempu1JeCKOU npozpeccuu S = _!!l__, lql< 1 1- q 06PA30BAHHE (a±b)2 = a2±2ab+b2; (a±b)3 = a3 ±3a2b+3ab2±b3 WIU (a±b) 3 = a3 ±b3 ±3ab(a±b); a 2 -b2 =(a-bXa+b); a 3 ±b 3 =(a±bXa 2 + ab+b2} (a±b±c) 2 =a2+b2+c2 ± ±2ab ±2ac + 2bc; (a±b) 2 =(a±bXa±b); (a-b) 2 =(b-a)2 flpOU3600Hble HeKomopbZX ¢YHKlfUU (a, b, k, C - nocmoRHHbte} , C' = O; (kx+b) = k; x' =1; (xn J=n·x"-1 ; (sin x)' =cos x; (cos x)' = - sin x; ( ) , 1 )' 1 tgx = - - ; (ctgx =--.-; cos2x sm2x ( ) , 1 , 1 lnx =-; (log0 x) =--; x x·lna (exJ=ex; (ax J= ax ·ln a; , 1 , 1 (arcsin x)= r:-7 ; (arccos x) = vl -x2 ~l-x2 ' ( , 1 , 1 arctg x) =- -2; (arcctg x) =- - - 1+ x l+x2 llpa6UJIQ ourj>rj>epem1upoeamm (u, v - rPYHKlJllll, c- nocmORHHGR) (Cv)' =Cv'; (u +v)' =u' + v'; ' (!!_v)' u'v - v'u(uv) = u'v +uv'; v2 (g(J(x)))' = g'(J(x))-J'(x), 2oe g(J(x))-CJZO:JICHCIJi rPYHKlJWI. TeoMempul/ecKuu CMblC!l npOU3BOOHOU f'(x0 ) = tg a =k 3tta'!eHHe IIpOHJBO,[l;HOii <i>YHJ<Uml B TO'IKe paimo yrJJOBOMY K03<t><t>mi:HeH'ry KacaTeJJbHOii K rpa<i>HKY cpyttKUHH B3TOii TO'll<e. <PU3U'leCKUU CMblCR npOU3600HOU v(t)= s'(t) CKOpOCTb - npOH3BO,[l;H3R OT KOOp,a:HH3Tbl IlO epeMeHH. a(t)= v'(t) y CKOpeHHe - npoll3BO,a:H3R OT CKOpocnt no epeMeHH. YpaeHenue KacamenbHOU Ypaetteu11e KacaTeJJbHOH K rpa<t>11Ky <i>YHKUH11 f e TO'!Ke rpa<t>11Ka c a6cuttccoii x0 y = J(xo)+ f'(xoXx-xo). )],JUI mo6hIX H3T)'pa.JihHhIX n 11 k, 6oJibllll1X 1, 11 mofihrx a ~ 0 11 b ~ 0 septthI paBeHCTBa: ef;;f; = ef;.efb,. (ef;} = W: Vf= ~ (b *o); w=:= ef;; Va= ef;i,. (Var =a; Va< efi;, ecJIH 0 ~a< b; 2ef;F=la!: 2n+r-;; = _2n+J; a_r;:. =Y,mEZ,nEN Ecm1 m<O, TO a>O, ecJrn m>O, TO a~O Ta6nu1Ja nepBoo6p03HblX HeKomopbtX PYHKIJllU (a, k, C - nocm011H11ble) <f>yHKIJ;IDI f(x) ITepsoo6pa3HaJI F(x) k kx + C x", (n E Z,n * -1) n+I _x_+C n+ 1 1 2,J";+C..fX SlDX -cosx +c cosx sinx + C 1 tgx+ C--- cos2 x 1 - ctgx + C- -- sin2 x 1 Inlxl+c- x ex ex+ cx ax ..E_ +C 1n a flpaBuna Haxo:J1Coe11UJ1 nepeoo6p03HblX: I . EcJIB F - nepBoo6p33H3R ,!IJIJI f, a G- nepsoo6p33HaR ,!IJIJI g, TO F + G eCTh nepeoo6p33H3R ,!IJIJI/ + g. 2. EcJJH F - aepBoo6p33H3R ,!IJIJI f, a k - nOCTOHHHaR, TO <i>YHKUHJI kF eCTb aepeoo6p33HaJI JJ.JU! kf 3. EcJIH F(x) - nepeoo6p33tta)[ ,!IJIJI ftx), a k *0 H b - noCTOHHHble, TO 1 - F(kx+b) ecTb nepsoo6pa3HaR k ,!IJIJIJ(kx + b). <PopMyna Hb10m0Ha - Jleu61-1u1Ja EcnH F- nepsoo6pa3Hfill .llllil/Ha [a;b], To b fJ(x) dx = F(b)- F(a) a HeKomopb1e cBoiicmBa uHme2pana b b fkf(x)dx =k_- ff(x)dx; a a b b b f(J(x)+g(x))dx= ff(x)dx+ fg(x)dx a a a
  • 2.
    0cH06Hble </Jop.i1ynbl 2 22 1 7! sin x +cos x = l; 1+ tg x = --2 -, x =t - + nn, n E Z; cos x 2 . sin x 1! cos x tgx =-·-, x =t-+nn, n E Z; ctgx =-.-,x=t nn, n E Z; cosx 2 sm x nn 2 1 tgx·ctgx = 1, x =t-, n E Z; l+ctg x =-.-2 -, x =t nn, n E Z. 2 sm x <PopMyRbl CRO:J/CeHUJl sin (x ± y) = sin x cosy±cos x sin y; cos (x ± y) = cos x cosy+ sin x sin y; ( + ) tg x ± tg y 1! tg x_y = , x, y, x±y=t-+nn,neZ 1± tg xtg y 2 <PopMyRbl OJIJI KpamHblX y2J106 sin 2x = 2 sin x cos x; sin 3x = 3 sin x - 4 sin3 x; cos 2x = cos2 x-sin2 x = 2cos2 x-l = 1-2 sin2 x; cos3x=4cos3 x-3cosx; tg2x= 2 tg~ ,x=t 1! +nn,neZ 1-tg x 2 sin2 ~ 2 <PopMyRbl nonoeuHHOZO apzyMeHma 1- cos x 2 x 1+ cos x cos - 2 2 2 x sin x tg-=--- 2 1+cos x 1-cosx x =t 1! +2nn, n E Z sin x </JopMyRa OOnORHUmeRbHOZO y2lla a sin x + b cos x = ~a2 +b2 sin (x+rp), rlJ,.e rp =arctg~ a 3HGKU mpuzoHOMemput/eCKUX </JYHKlfUU sin a cos a tga H ctga arcsin(- x) = - arcsin x; arccos(- x) = ;r - arccos x; arctg(- x) = - arctg x; arcctg(- x) = ;r - arcctg x; arcsin x + arccos x = 1! npH !xi ::::; 1; arctg x + arcctg x = ,. ; 2 2 sin(arcsin x) = x rrpw lxl ::::; 1; cos(arccos x) = x, ec.JIB lxJ ::::; l; arcsin(sin x) = x rrpw !xi::::;!!_; arctg(tg x) = x npH I~< 1!; 2 2 arccos(cos x) = x npH 0::::; x::::; ;r; tg(arctg x) = x rrpw x ER; ctg(arcctg x) = x; arcctg(ctg x) = x, ecJilf 0 < x < ;r. ao oo 30° 45° 60° 90° 120° 135° 150° a' pa,11, 0 tr 16 tr 14 tr /3 tr /2 2 tr /3 3tr 14 5tr16 sin a 0 I Ii. .f3 I .f3 Ii. I - - - - - - 2 2 2 2 2 2 .f3 Ii. I I Ii. .f3cos a I - - - 0 -- - - - - 2 2 2 2 2 2 I .f3 -Ji 1 tga 0 .f3 1 - - 1 -J3 .f3 I I -Jictga - 1 J3 0 - .f3 - 1 180° tr 0 - 1 0 - <Pop,i1y.?bl npeo6pG306aHUR cyMMbl e npoU3eeoeHue . . 2 . x+y x-y smx+silly= Sill--cos--; 2 2 . . 2 . x-y x+ y Sill x - Silly= sm--cos--; 2 2 x+y x-y cos x +cosy= 2 cos--cos--; 2 2 2 . x+ y . x-y cos x - cosy=- sm--sill-- · 2 2 , sin(x±y) 1! tg x ± tg y = , x, y =t - + tm, n E Z; cosxcos y 2 sin (y±x) ctg x ± ctg y = . . , x, y =t nn, n E Z smxsmy </JopMyRbl npeo6pG30BGHUJl npoU3eeoeHUR 6 cyMMy sin x ·sin y =2-(cos(x- y)- cos(x + y )); 2 cos x ·cosy =2-(cos(x - y )+ cos(x + y )); 2 sin x ·cosy =2-(sin(x - y)+ sin(x+ y )) 2 YHu6epCGllbHG5l noocmaH06KG 1- tg 2 ( ~) . 2 tg(~) COSX= (x) ' s1n x = ( x)' 1+ tg2 - 1+ tg2 - 2 2 x =t 1! +2nn, n E Z <PopM)IRbt npueeoeHuJ! tr tr 3tr a tr-a tr+a --a -+a --a 2 2 2 sin a sin a - sin a cos a cos a - cos a cos a - cos a - cos a sin a - sin a - sin a tga - tga tga ctga - ctga ctga ctga - ctga ctga tga - tga tga 0 I Ii. .f3a - - - 2 2 2 arcsma 0 tr16 tr /4 tr /3 arccosa tr 12 tr /3 tr /4 tr 16 3tr -+a 2 - cos a sma - ctga - tga I tr 12 0 1 .f3a 0 .f3 1 arctga 0 tr 16 tr /4 tr /3 arcctga tr 12 tr /3 tr 14 tr16 270° 3 tr /2 360° 2tr sin(- x) = - sin x; ctg(- x) = - ctg x - 1 0 0 I - 0 0 - 11HcjJOpMa~•OHHO·cnpaao•Ha• ra6nu~a © 000•l1Hcjlonnacr•, 2007 r.Moc<aa, Kawupc<oe wocce,21 E-mail: mail@infoplast.ru Http://www.infoplast.ru 0 '° no.anucaHO 8ne.arb 09.02.09. Tupax 40003K3. 3aKa3 ~ 34555. 113,llarenb 000 •l1Hcjlonnacr•, MOCKBa, KawupcKoe wocce, 21. Ten./<PaKc: 8(495) 730·01·87. TunorpacP•• 000 •B•aa·Crap•. 107023. MOCKBa, yn. 3neKTµOJaBD,QCKa•. 20.
  • 3.
    log0 b =c (r,11,e b>O, a>O, a 7= I) Tor,11,a H TOnbKO Tor,11,a, Kor,11,a ac= b. Oc11oe11oe 1w2apurj>Mu1JeCKOe moJ1Coecmeo alogab =b Ceoucmea Rozapurf>1110e (a> 0, a* 1, b > 0, c > 0) log0 l = O; lo~a = l; log0 (bc)= log0 b+log0 c; log0 ( %J=log0 b- log0 c; k log0 b =k ·log0 b; ecm1 k-qeTHoe: log0 bk=k·log0 lbl lo b = logcb (c 7= 1); ga logea log b=-1- (b7=l); a logba log nbk=!·log b a n a ax2 + bx + c = 0, a7= 0 D = b2 - 4ac - oucKpUMu11a11m Kea,n,paTHoro ypaettemrn. Ecm1 D < 0, To ypaettem1e He KMeeT .ueM:CTBJ1'TeJihHhIX KOpHeH. Ecnu D = 0, TO ypaeHem1e KMeeT 1 KopeHh b x=-- 2a Ecm1D > 0, TO ypaeHeH11e 11MeeT 2 KOplUI: - b+Ji5 -b-Ji5 XI= ' X2 = 2a 2a TeopeMa Buema Ecn11 rrpHBe.uettttoe KBa,n,parnoe ypaetteHlfe x2 + px + q = 0 KMeeT KOpHH Xi H X2 (T.e. D;::: 0), To X1 +X2 =-p, X1 ·X2 =q TeopeMa, 06pam11QJ! meopeMe Buema EcnH <rncna m 11 n TaKOBbJ, '!TO m + n =-p H m .n =q' TO JTH 'lHCna llBJllllOTCll x2+px+q=O. KOpID!MH ypaetteH11ll Keaopam11oe ypGfme11ue c 'lemHblM 6mOpbL111 K03rj>rf>ulfUeHmOM ax2 + 2kx + c = 0, 2oe b = 2k D*=k2-ac, (n*=±nJ * -k±.JD*Ecrrn D > 0, TO x1•2 = - - - - a k ecJIH D* = 0, To x = -- a PQ3J10:J1Ce11ue K6aopam11020 mpex1JJ1e11a Ha MHOJ/Cume.m Ecnu X1 If X2 - KOpHll KBa,n,paTHOro Ipex'l.netta a:l + bx + c, To a:?-bx - c = a(x - x J (x - x::) y=kx y=kx+b y = ax2 y =ax3 y=~ x ~ ~ __i1L; ---;r::o x y k < o/ . ___./ ~ o (........ x y = smx y y = cosx y y=tgx y = ctgx 2. 3. 4. • ecJll1 a < 0, TO peweIDlii HeT; • ecn11 a = 0, TO x =O; • ecm1 a > 0, TO x =±a. Ix - bl =a • ec1rn a < 0, TO perneHlfi1 HeT; • ecJIH a = 0, TO x =b; • ec1rn a > 0, TO x = ±a+b. ( 'I ( 'I [/(x) = g(x), If x,, =lg x,, <=> J(x)= -g(x} ![ /(x) = g(x), IJ(x~=g(x)<=> J(x)=-g(x), g(x);::: 0. • ecJrn b > 0, TO x = log0 b • ecm1 b ~ 0, TO pewem1i1 HeT y=ax 2. af(x)= bg(x)<=> J(x)· logca = g(x)· logcb, r.Qea > 0, a 7= 1, b > 0, b 7= I, c > 0, c 7= 1 B '1acm11ocmu, ypae11e11ue af(x)= ag(x)<=> J(x) = g(x) rx)}>O3. (u(x))f(x)= (u(x)f(x)<=> (u(x)) otl, J(x)= g(x) (npH a> 0, a 7= 1) 1. log0 f (x) = b <=>f (x) =ab 2. log0 f(x)= log0 g(x)<=> <=> ({/(x) =g(x), HnM {f(x) =g(x),J J(x)> 0. g(x)> 0. (J11H peuieHWI OaHH020 ypatmeHWl nepexoaam mo.1&1w >r odHaii 113 :)lflU:X cucme.v moii. KOmopall npo114eJ). I. 2. I. • • • • • 2. • • y (x-a)2 +(y-b)2 = R2 ~ ~ .[fW= g(x)<=> {f(x)= g 2 (x), g(x);::: 0 .fiW= M;'J <=> { f(x) = g(x), <=> J(x);::: 0 (11n11 g(x);::: o) sinx= a ecnH lal > I, TO peweHHii HeT; ecm1 lal ~ 1, TO X = (-lrarcsin a+trn, n E Z l..facm11b1e CJ1y1Jau: sin x = 1, x = tr +2m1, n E Z 2 sin x = 0, x =m1, n E Z sinx=-1 x=-~+2m1 nEZ , 2 ' cosx= a ecm1 lal > l, TO peweH11i1 1rnT; ecm1 lal ~ 1, TO x =± arccos a+ 2m1, n E Z L/acm11b1e cRyl./au: • cos x = 1, x =2m1, n E Z 7r • COS X = 0, X = - +ml, n E Z 2 • cosx=-1, x=tr+2m1,nEZ 3. tgx=a, x=arctga+ m1,nEZ 4. ctg x =a, x = arcctg a + m1, n E Z
  • 4.
    KeaApaTHb1e HepaeeHCTea HepaeeHcTeac MOAyneM Jlorap111Q>M111"tecK111e HepaeeHCTBa (a* 0) (npHBOllllMbie K BHl1)' ax2 +bx+ c > 0, ax2 +bx+c2':0 , aX'+bx +c <O, ax2 +bx+cSO) fpa<j>HKOM <j>YHJG.lffl1 f(x) = al-+bx+c l!BnlleTCll napa6ona; KOOpt111HaTbl eepllll1Hbl b D Xo =--, Yo= f(xo)= -- 2a 4a ,Lilll peweRl1JI KBat(paTHOro HepaseHCTBa BbI<rnCnlllOT A11CKpHMHHaHT D H onpet1eilJl10T KOpHH KBat1paTRoro TPi!x•rneHa. • D<O 11 a>O HepaeettcTeo ax2 + bx + c > 0, ax2 + bx+ c :::0: 0 ax 2 + bx + c < 0, ax2 + bx+ c ~ 0 • D<011a<O HepaeeHCTBO ax'+ bx+ c > 0, ax 2 + bx + c z 0 ax 2 + bx+ c < 0, ax2 + bx+ c ~ 0 • D = 011a > O Hepaaettcrno ax 2 + bx+ c > 0 ax2 + bx+ c z 0 ax2 +bx+c<O ax2 + bx+ c ~ 0 • D=O 11 a < O HeoaeeHcTeo ax2 + bx+ c > 0 =2+ bx+ c z 0 ax2 + bx+ c < 0 =2+ bx+ c ~ 0 • D > 011a>O HepaaettcTeo ax2 + bx + c > 0 ax2+bx+c z 0 ax2+bx+c < O =2+ bx+ c ~ 0 • D>O 11 a<O Heoaeettcrno ax2 + bx+ c > 0 ax2 +bx+c < O ax2 + bx+ c ~ 0 OTBeT XER XE0 XER Xo 0TBeT XER XE0 X=X0 Xo ( " OrneT XE0 X =X0 XER I J x~2 x OrneT OrneT 1. 2. 3. 4. 5. x 2. 3. 4. 5. 2. 3. Ix-bl< a • ecn11 a s 0, TO perneHHH HeT; • ec1m a > 0, Tob-a<x<b+a Ix - bl 2: a • ec1m a s 0, TO x E R ; • ecmi a > 0, TO [ x:::O:b+a, xsb-a IJ(x) < g(x) <=> {f(x) < g(x), f(x)> -g(x) If(x) > g(x) <=> [f(x) > g(x), J(x)<-g(x) IJ(x) > lg(x) <=> f 2 (x)> g 2 (x) • ec.Tl11 a~ 0, TO pernemrn tteT; • ecJIB a > 0, TO 0 s x < a 2 /;>a • ecn11 a < 0, TO x :::0: O; • ecnn a = 0, TO x > O; • ec1m a > 0, TO x > a 2 { f(x):::o: 0, [.M < g(x)<=> g(x)> 0, f(x)< g 2 (x) { g(x):::o: 0, rrr::;. ( ) f(x) > g 2 (x); 1JJ -'-} > g x ¢:> { g(x)< 0, f(x):::o: 0 rrr::;. CC {f(x) > g(x), 1JJ-'-J>1JgXj¢:> () g x :::o:o • ecfill m s 0, a > 0, a *I, TO perneHHH HeT; • ecJm m > 0, 0<a<1, TO J(x) > loga m; • ecim m>O,a>I, TO J(x)<logam af(x)> m • ec1m m s 0, a > 0, a *I, TO XE D(f); • ecm1 m > 0, 0 < a < 1, TO f(x)<logam; • ecnH m > 0, a > l, TO f(x)>logam af(x)> ag(x) • ecirna> 1, TO f(x) > g (x); • ecnHO < a<l , TO J(x) < g (x) l. 2. (mER) log0 f(x) < m • ecJIB 0 <a< 1, TO f(x) >am; • ecn11 a > l, TO {f(x) < am' f(x)> 0 logaf(x) > m • ecim 0 <a< 1 TO {J(x)< am, ' J(x)> O; 3. 4. • ecfill a> 1, TO f(x) > am log0 f(x) > logag (x) • • ecsrnO<a < l, TO { / (x) < g(x), J(x)> O; ecilll a> 1, TO {f((x))> g(x), g x >0 logh(x)f(x) >log h(x)g(x) <=> l h(x)> 0, h(x)< 1, J(x)< g(x), <::> J(x)> O; l h(x)> 1, J(x)> g(x), g(x)> 0. l-Illcno nepeCTaHOBOK 113 n 3ilCMCHTOB P. =1·2-. ..-(n - l)·n=n! l{Hcno coqeram1ii 113 n 3neMeHTOB no m Cm= n! . Co=l n m!(n - m)!' n CeoiicTea coqeTaHHii Cm= Cn- m. Cm+Cm+I= Cm+I n n ' n n n+l l-Illcno pa3MCII.lCHHH 113 n 3JleMCHTOB no m Am= P ·Cm= __n_!_ n m n (n - m)! <l>opMyna 6HHoMa lliIOTOHa (a+br = c0 an+C1 an- lb+ ... n n C k n- kbk en bn...+ na +...+ n Hill1 ( b)n n n- lba+ =a +na +... n(n-1)...(n - k+l) n- kbk bn ...+ a +...+ k! I')J.C nEN H c;an- kbk = Tk+I CCTb (k + 1) - if 'IJICH B pa3JJOJKemrn 61rn0Ma (k = 0, 1, 2, ... , n) CyMMa 6HHoM11Han&RbJX K03<j>cl>mv1eHTOB pasHa 2n: c~ + c~ +... +c: = 2n '1HcjJopMaljHOHHO-Cnpaa04Ha5i ra6m14a © 000 •'1HcjJonnacr•, 2004 r. MocKea, KawHpcKoe wocce, 21 E-mail mail@infoplastru Http:l/www. infop/astru Ten.: (095) 320-94-89 0axc: (095) 320-94-88 ----- ·~--- 00 N 0 0
  • 5.
    • 0 6 PA 3 0 8 A H V1 E l'fc. ) or ) _I ( ,,.,,; - - ' -f )( . - 'f ·) l ~www:1nfopl.ast.ru (f 6 - l/f?t) - (// ~O / - - ./ ~ .c....... ...... ..,,.........,...,,i.,. OnpeAeneHMe KOMnneKcHoro 'IMcna OnpeAeJleHMe1. LIVICJla BVIAa z=a+bi, rAe a VI b - AeiACTBVITeJlbHble 'iVICJla, i - MHV1Ma51 eAVIHVIUa, 6yAeM Ha3blBaTb KOMnneKCHb/MU. 0603HaYeHVle a= Rez, b=Im z. L!V1c11a z= a+ib VI z = a - ib Ha3blBatOT conpfl>K8HHb/Ml1. 3anVICb KOMnneKCHOro 'iVICJla B BVIA8 a+bi Ha3blBaeTC51 anre6pal1'18CKOU cjJopMoft KOMnlleKCHOro 'il/ICJla. LllllCJlO a 6yAeM Ha3BaTb JJ.8MCTBl1T8flbHOft '1aCTblO KOMnneKCHOrO 'iVICJla, bi - MHUMOU lfaCTb/O KOMnlleKCHOro 'iVICJla, b - K03cjJcjJ114ueHTOM npu MHUMOU l/aCTU. B03MO>KHbl cnyYaVI, KOrAa A8ritCTBVITeJlbHble 'iVICJla a VI b MOryT 6b1Tb paBHblMVI HYJllO. ECJlVI a= 0, TO KOMnJleKCHOe 'iVICJlO bi Ha3bl- aaeTC51 l/UCTO MHl1Mb/M. ECJlVI b= 0, TO KOMnJleKCHOe 'iVICJlO a+bi paBHO a VI Ha3blBaeTC51 JJ.8UCTBUT8flbHb/M. ECJlVI a=OVI b=OOAHOBpeMeHHO, TO KOM- nneKCHOe Y111c110 O+Oi pasHo Hy11t0. jJeftcraurenbHbte l/ucna /If l/11cro MH11- Mb1e '111cna npeJJ.cTaBnHIOT co6oft l/aCTHbte cny'1a11 KOMnneKCHoro l/11cna. Asa KOMnneKCHblX YV1c11a a+bi VI c+di yc11oa11111V1Cb CYVITaTb paBHbtMl1 TOrAa Ill TOJlbKO TOrAa, KOr,[a B OT,[8JlbHOCTVI paBHbl VIX ,[8lACTBVITellbHbl8 YaCTVI VI K03cpcpV1UVleHTbl npVI MHVIMOrlt 8,[l/IHVIUe, T. e. a+bi= c,+di, eCJlVI a=c VI b=d. 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Af151 3TOrO Bbl6e- peM Ha n110CKOCTVI A8KapTOBY np51MOyrOJlbHYIO CVICTeMy KO- OPAVIHaT. OCVI Ox VI Oy Ha3blBalOTC51 COOTBeTCTB8HHO A8ritCT- BVIT8JlbHOrlt VI MHVIMOl/t OCblO. .0 ~ 0 ~ y b PMCYHOK 1 z(a ·b)- - - - - J Ka>KAOrit TOYKe nnOCKOCTVI c KOOPAVIHaTaMVI (a; b) COOTB8TCT- ayer OAlllH VI TOJlbKO O)J,VIH 88KTOP c HaYaJlOM 0(0; 0) VI KOH- UOM z(a;b). no3TOMY KOMnJleKCHOe YVICJ10 z= a+bi MO>KHO Vl306pa3VITb 8 BVIAe BeKTOpa c HaYaJlOM 8 TOYKe 0(0; 0) VI KOHUOM 8 TOYKe z(a;b). ~ ~ 0 a x ,lleucmeume.ttbH(JJI, ocb TpMrOHOMeTpM'leCK3SI (j>opMa KOMnneKCHOro 'IMCna KoMnneKCHOe Y111c110 z= a+bi Vl306pa>KeHo 8 BVIAS BSKTopa c HaYaJlOM 8 TOYKe 0(0; 0) VI KOHUOM z(a;b) (p11c. 3). OnpeAeJleHMe 3. Mo/J,yneM KOMnlleKCHOro YVIC- na z= a+bi Ha3blBaeTc51 AJlVIHa aeKTopa, KOTO- pyto MO>KHO HarltTVI no cpopMyne r= lzi=.Ja 2 +b 2 , (MOAYllb KOMnJleKCHoro YVIC- Jla 0603HaYeH 6yKBOrlt r). OnpeAeneHMe 4. ApryMeHTOM KOMnneKcHoro YV1c11a Ha3braaeTC51 yron cp, KOTOpbrrlt 06pa3yeT B8KTOP c noJlO>KVITeJlbHblM HanpasneHVleM OCVI a6CUVICC. Bellt.1'it.1HY yr11a <P MO>KHO HarltTVI c no- m a . b 3MOl.J.lblO '+'OPMYJl: cos<p = r VI Stn<p = r. Ta CVICTeMa VIMeeT 6eCYVICJ18HHOe MHO>K8CTBO pe- weHl/lrlt BVIAa cp+2nk, rAe k- 11to6oe uenoe YVIC- 110. TaKVIM o6pa30M, Jlto6oe KOMnJleKCHOe YVIC- 110 z VIMeeT 6eCKOH8'iHOe MHO>K8CTBO apryMeH- TOB, OTJlVIYalOl.J.IVIXC51 APYr OT p,pyra Ha 'iVICJlO, KpaTHOe 2TC. ECJlVI k= 0, TO Mbl nonyYVIM rllaB- HOe 3Ha'i8HVl8 apryMeHTa cp, KOTopoe VI 6yAeM Ha3blBaTb apryMeHTOM KOMnJleKCHoro 'iVIClla. ECJlVI B 3anVICb KOMnJleKCHoro 'iVICJla z BMeCTO a t.1 b nOACTaBVITb 3HaYeHVl51 a= rcoscp , b= rsincp , TO nonyYVIM HOBYIO cpopMy 3anV1CVI KOMnneKcHoro YV1c11a: z =r(coscp + isincp)I KOTOpa51 Ha3blBaeTC51 rpuroHOMeTp11'18CKOH cjJopMOH KOMnJleKCHoro 'iVICJla. npasMno nepexoAa or anre6paM'tecKoH ctJopMbl KOMnJleKCHoro 'tMCJ13 KTpMrOHOMeTpM'teCKOM: 1. HaXOA51T MOAYllb KOMnJleKCHOro 'iVICJla r, AJ151 Yero VICnOJlb3YIOT cpopMyJly r = Ja 2 +b2 . 2.An51 Haxo>KAeHVl51 cp cHaYana onpep,e1151toT reo- MeTpVIYeCKVI, 8 KaKorlt 'i8TBepTlll HaxOAVITC51 TOYKa z. a . b 3. CocTaBn51IOT ypaaHeHVl51 coscp= r ' Sincp = r VI no peweHVllO OAHOro 1113 HI/IX HaXO)J,51T yron cp. 4. 3anVICblBatoT KOMnJleKCHOe 'iVICJlO z 8 TpVlrO- HOMeTpVIYeCKOrlt Q:>opMe. npeACTaeneHMe cyMMbl, npOM3BeAeHMSI M'13CTHOro. CreneHM MKOPHR. (n= 0, I, 2, ...) Ec11V1 p,aHbl z1= r1(coscp1+ i sincp1) 111 z2 = r2 (coscp2 + i sin <p2 ), TO z1•z2= r1r, (cos(cp1+ cp2) +i sin(cp,+ cp,)); • C11o>KeHV1e KOMnlleKCHblX YVIC8Jl z,= a,+ib, VI z2= Cl1+ib2. z1+z2= a 1+ib1+a2+ib2= a1+a2+i(b1+b2); • Pa3HOCTb KOMnJleKCHblX YVICen z,= a,+ib, VI z2= a2+ib2. z,-z2= a1+ib,-a1- ib2= a,- a2+i (b,-b2); • YMHO>K8HVl8 KOMnJleKCHblX 'it.1C811 Z1Z2= a,a2-b1b,+i(b1a2+b2a) a1+ ib1 -- a 2 + ib2 = (a,a2+h1b2 ~+ i(~2b1- a1b2) ' (z2¢0) . a2+b2 nocneAOBaTenbHOCTM ECJlVI paccMOTpeTb P51A HarypaJlbHblX YVIC8Jl 1, 2, 3, ..., n, ... VI 3aMe- HVITb Ka>KAOe HaTypanbHOe 'iVICJlO n 8 3TOM P51AY HeKOTOPblM 'i~C­ llOM a., CJleAY51 HeKOTOPOMY 3aKOHy, TO Mbl nonyYVIM HOBblrlt P51A YVl- cen a 1, a1, ..., a._1, a01 ... , KpaTKoe o6o3HaYeH~e {a.} VI Ha3blBaeMblrlt 'iVICJlOBOrlt nocneAOBaTeJlbHOCTblO. OrpaHM'teHHbte noc11eAOBaTe11bHOCTM 1) OrpaHVIYeHHa51 caepxy, TO eCTb Cyl.J.leCTByeT B, TaK, YTO a,,sB, A1151 11to6oro nEN. 2) OrpaHVl'ieHHa51 CHVl3y, TO eCTb CY1.J.18CTBY8T A, TaK, YTO As b,,, AJ151 11t06oro nEN. ; 1 = r1r1[cos(cp1+cp2) + i sin(<p1+cp2)] , z" = r" (cos(ncp)+ i sin(ncp)); (n - 4e11oe YVICJlO) (ctJopMyna Myaspa). 2 n r .!. .. 'Pl(, cp+2kn . . cp +2kn)Ec11V1n - HaTypa11bH08YVICJlOVl z ¢0, TO v z =zn =v1z1lcos n + zsin n , rAe ~ - apV1cpMeTVl'i8CKVlrlt KOpeHb Vl3 nOJlO>KVITellbHOro 'iVICJla lzl, cp= arg z VI k=O, l , 2, ..., n-1 . 0 "l - 2kn . 2kn ,,~ 1 _ (2k+ l)n . l2k+ l)n ( _ . k-O )TM8TVIM, YTO vt - cos n +sin n, v-1 - cos n +srn n , n - L,2, ..., - , l , ..., n- 1. npeAenb1 nocneAoearenbHOCTM OnpeAeneHMe: YVICJlO a Ha3braaeTC51 npeAenoM 'iVICJlOBOrlt nocneAOBaTeJlbHOCTVI a., 8CJ1VI AJ151 Jlto6oro CKOJlb yrOAHO Manoro 'iVICna E> 0, Harlt- AeTC51 HaTypallbHblrlt HOMep N TaKorlt, YTO AJ151 acex YV1ce11 n?:.N Bb1no11H518TC51 MOAYllb pa3HOCTVI la.-al<E ~ V c>O3 N: V n?:.N=:> la,,-al<e. HaYVIHa51 c 3Toro HOMepa N ace YV1c11a 3TO~ nocne- AOBaTellbHOCTVI nonaAatOT 8 E OKpeCTHOCTb 'it.1C- 11a a. .QpyrVIMVI CJlOBaMt.1, HaYVIHa51 c HOMepa N BHe VIHTepaana a- e; a+e MO>KeT HaxOAVITbC51 He 6011ee KOHeYHoro 'iVICJla YJ18HOB nocnep,oaaTeJlbHOCTVI. lima,, =a 1r->oo TeopeMbl o npeAenax 'IMCnOBblX nocneAoearenbHOCTeH 3) OrpaHVIYeHHa51, TO ecTb cy~ecTayeT A, B, TaK, YTO Asa.s 8, AJ151 11t0- 6oro nEN, ~ cy~ecTayeT C>O, TaK, YTO la.l<C, AJ15111to6oro nEN. ECJl~ {a.} VI { b.} - AB8 CXOA51~~eC51 nOC118AOBaT8JlbHOCTt.1, TO: limc·an = c lim an= c·a , (c - 'i~CJlO); n~ n~ TeopeMa 0 npeAeJle CYMMbt: nycTb liman=a I limb,,= b ==!;> lim(a,, ±b,,) = liman + limbn= a+ b; MOHOTOHHbte nocneAOBaTeJlbHOCTM 1) so3pacTat01.J.1aH a.<a.-1, V nEN. 2) y6b1Bat01.J.1a51 a,,>a0 _ ., V nEN. 3) He B03pacTato~a51 a.>a•." V nEN. 4) He y6b1Bato~a51 a. sa•." VnEN. n-+«> 11 -+<:io n~ n~ n--+«i TeopeMa 0 npOM3BeAeHMe npeAenos: nycTb limall=a , limbll=b ==!;> lima,, ·bll = lima,, ·limb,, = a·b; 11-+<0 n-+<0 11-+oo JJ -+oo 11-.00 lima,, TeopeMa 0 npeAeJle 't3CTHOro: nycTb lima,,=a, limb,,=b, b¢0 ==!;> lim!£.bn = n~ n-+00 11-+«> n-t-oo ,, 11mb,, n-+OO a b' •
  • 6.
    OnpeAeneewe npeAe.na xcno1oilt>JBDIDI. DA110CTopo11111e npeAenllt. CaoicTBa npeiienos L11cno .4 Ha3olBaeTCSl 1pe,[1e1101.1 ¢>Y'r!KL.1H'1 _r-_Il.rl B TO'-iKe .T. ecn MAflSi lll060~ nOCfi8A0- 8aT811bHOCTM AOnyCTl1MblX 3HaYeHl1~ apryMeHTa Xn• (.t , ¢ Xo), CXO,[IS1ll!8~CS1 KXo 2) CYMMa KOHe'iHOro 'tMCfla 6.M. Yl1C8J1 eCTb 6.M. Yl1CJ10; 3) npe,Qe11 cyMMbl pa0eH cyMMe npe,Qenos Jim(/(x) + g(x)) = lim/(x) + lim g(x); x->xo x->.lo x-..t-0 (T.e. limxn=xo). noc11e,[I08aTeJlbHOCTb COOT88TCT8YIOll!l1X 3HaYeHll1C1 cpyHKL.1111111 /(x,,), n-+x 4) npe,Qen npo11130e,L1eH1115I paseH npo11130e,QeH11110 npe,Qe1100 lim/(x) ·lim/(x) = lim (J(x) ·g(x)) ;11 E N, CX0,[1111TCS1 K Yll1CJ1Y A, T.e. Jimf(x) =A. reoMeTpll1'-l6CKll1C1 CMblCJ1 npe,[lena 3TOC1 x~.to .t-+x0 x->.to x->xo cpyHKL.1111111, '-ITO,[11151 8C8X TOY8K X, AOCTaTOYHO 6111113Kll1X K TOYKe Xo, COOT88TCTBYIOll!ll18 3Ha'-leHll1S1 cpyHKL.1111111 KaK yrOAHO Mano OTJ1111YalOTC51 OT Yll1CJ1a A. 5) KOHCTaHTbl MO)KHO BblHOCll1Tb 3a 3HaK npe,L1e11a Jim c·f(x)= c·lim.f(x)' (c- Yll1C110); x->x0 .t->Xo f(x) Jim .f(x) 0AHOCTOPOHHHe npeAenbl. 6) lim = x-+xo ec11111 lim g(x) ?!O· Ct.t111raeTC5I, YTO x CTpeMll1TC51 KXo 11106blM cnoco6oM: OCTaBa51Cb M8HbWll1M, Y8M Xo (cnesa OT Xo). 60JlbWll1M, YeM Xo (cnpasa OT Xo). 111111i1 K011e611S1Cb OKOJlO TO'-IKll1 Xo. x-+xo g(x) lim g(x) ' x-+xo ' X4-Xo 7) ec111i1 Jim fix~ = 1, TO lim/(x) = limg(x) (/111 g Ha3blBalOTCS1 npe,Q811bHO 3K8!i1Ba-Y111cno A1 Ha3b10aeTcs:i npeAenoM ct>YHKl.IHH y f(x) cneBa B TOYKe ,t 0, ec11111A11S111106oro c<O CYll!6CTByeT Yll1C110 a=a(io)>OTaKoe, YTO np1i1 xE(xo-a;xo), BblnOJ1H518TCS1 Hepa- B8HCT80 l.f(x) - A1l<c, lim f(x)=A1 • X-+Xo- 0 x-.xo g X x.-.x0 x-+x0 118HTHblM!i1 np1i1 crpeMJ18Hll11i1 x KXo); npeAenoM ctJyHKl.IMM cnpaBa Ha3bl8a8TC51 8) 3aMeHa nepeMeHHoCl: nycTb ,QaHbl 03a111Moo6paTHb1e cpyHKL.11111i1 cp(x) 111 'l/J(x). Tor,Qa lim/(x)= lim /('V(t)). B YaCTHOCTll1 lim/(x) = lim/( 1 t);lim f (x) = Jim1(t 1 ). x-+x0 t-+cp(x0) x-+0 t-+oo x-+oo r-+0 'lfe>O, ::lcr=cr(e), 'If XE(x0 ;x0+cr) => lf(x) - A 2 i<s <=>Jim f(x)=A2x-+ x0+0 TeopeMa:.f(x)>g(x), B 0°(xo) 111 3 limf(x)=b 111 3 limg(x) = c. Tor,Qa b~c. CBOMCTBa npeAenoB. x-+x0 .r~x 0 np1i1 yCJ1081111i1, YTO np8,[1811bl lim f (x) Iii Jim g(x) CYll!8CTBYIOT 111 KOH8'-1Hbl: TeopeMa:/(x) < y(x) <g(x) 'if xE0°(x0) 111 3 lim/(x)= b 1i1 3 lim g(x)= b. x->.l'o .r-+x0.l'4-Xo .t-+.ro 1) ec111i1 npe,Qe11 Iimf(x)=a => f(x) =a+a. cpyHKL.111151 pasHa 3TOMY Yli1CJ1Y n1110c 6.M. Tor,[la limy(x) = b. x->xo lim/(x)=O <:::>'lfe>O, 3cr>O:lx- x0 l<cr => lf(x)-al<e, x->x0 HenpepblBHble li>YHKQHH HHX CBOMCTBa. lO'IKa pa3pb1Ba li>YHKQHM, KnaccH$MK3QHSI £ - CK011b yro,QHO Manoe Yli1CJ10, l.f(x)-al=a;.f(x)=a+a. • _ - 1 . sin x 1nepBblH aaMe'larenbHblH npeAen: 1m x = x-+0 nycTb cpyHKL.11i1S1 y-.f(x) Onp8,[18J18Ha B TOYK8 X0 111 8 He- KOTOpOC 0Kp8CTHOCTll1 3TOC1 TO'-IKll1. ¢yHKL.11i1S1 Y-'f(x) Ha3blBaeTCS1 HenpepblBHOill B TOYKe Xo, ecn1i1 CYll!8CTByer npeAen cpyHKL.1111111 B 3TOC1 TOY- Ke 111 OH paBeH 3HaY8Hli1IO cpyHKL.1111111 B 3TOill TOY- TO'IKH pa3pb1Ba Cl>YHKl.IMM - 3TOTOYKll1 B KOTOpblX Hapy- waeTC5l HenpepblBHOCTb cpyHKL.11i1111. TOYKa pa3pb1Ba Xo Ha3b1Ba8TC5l TOYKOC1 pa3pb1Ba 1 POAa cpyHKL.11i11i1 y f (x), ec111i1 B 3TOC1 TOYKe CYll!8CT8YIOT KO- H8l!Hble npe,[1811bl cpyHKL.1111111 CJleBa Iii cnpasa (OAHOCTO- POHHll18 npe,QeJlbl) lim f (x)=A, 111 lim f (x)=A2 . Bo3bMeM Kpyr pa,Q111yca 1, o6o3Ha'-1111M pa,L1111aHHY10 Mepy yr11a MOB '-lepe3 x nycTb O<X <n /2. Ha p111cyHKe IA.M l=sinx, ,Qyra 11B '-1111C- ··· 11eHHO pasHa 1..1eHTpa11bHOMY yrny X, IB C l= tgx. Tor,Qa s s s }. 1 1 !>MOB < ceKmopa MOB < 6.COB, 2 Slll X < 2 X < 2 tgx · Pa3,Qe11111M see Ha 2 1sinx > O 111 no11yt.t111M: 1< .x < 1 . Sill x cos x I COS X < Sl~ X < 1. T.K. limcosx= 1, TOno npll13HaKy CYll!BCTBOBaHli1S1 npeAe11os X->0 . C118AY8T lim Sl~ x = l . X-+0 c M O cosx A B a Jim ~ = 0 (aER, b>l); X-++oo b lim !In= I· '11-++co tan l lim 1 n = 1. 11-+00 -n Ke: lim/(x ) = f(x0) . x->."o 3ro 03Hat.taeT: • cpyHKL.11i151 onpeAeJleHa B TOYKe Xo 111 B ee OKpe- CTHOCTll1; • cpyHKL.11i1S1 111Meer npe,Qen np111 x-x0; • npe,[1811 cpyHKL.1111111 B TOYKe Xo paBeH 3Ha'-18Hli1IO cpyHKL.1111111 B 3TOC1 TOYKe, T.e. BblnOJ1HS18TCS1 pa- B8HCT80. 3TO 03HaYaeT, '-ITO np111 HaXO)K,[18Hli1111 npe,Qena HenpepblBHO~ cpyHKL.11111i1 f (x) MO)KHO nepeC1Tll1 K npe,Qeny nOA 3HaKOM cpyHKL.1111111, TO eCTb B cpyHK- L.lli1111 .f(x) BMBCTO apryMeHTa x nO,[ICTa- Bli!Tb npe,[1811bHOe 3HaY8Hll18 Xo. • X-+Xo-0 X-+Xo+O np111 3TOM, ecn111: • A1=A2TO TOYKa Xo Ha3blBaeTCS1 TO'-IKOl-1 ycTpaH!ilMOro pa3pb1sa; • A1¢ A2TOTOYKa Xo Ha3blBaeTC5l TOYKOC1 KOH8'-IHOro pa3- pb1Ba. IA1-A2I Ha3b1saercs:i cKaYKOM cpyHKL.1111111. TO'-!Ka pa3pb1Ba Xo Ha3b1Ba8TCS1 TO'-IKOl-1 pa3Qb1Ba 2 pona cpyHKL.11111i1 y f(x), ec11111 no Kpail!Heill Mepe OA111H 1113 O,[IHO- CTOPOHHll1X npeABJlOB (cnesa 111Jlli1 cnpasa) He CYll.8CTBY- er, 111i160 paseH 6eCKOH8YHOCTll1. • Jt' • -! .... TeopeMbl 0 cpeiiHeM. npaeMno nonHTanSI PaccMorp1i1M cnoco6 pacKpb1T111s:i Heonpe,L1e- 11eHHocTeC1 0/0 Iii oo/oo, KOTOPblill OCHOBaH Ha npli1M8H8Hll1111 npO!i13BO,[IHblX. npaBHno nonMTanH, npH O/O. nycTb ctJYHKl.IHHf(x) Hcp(x) HenpepblBHbl H AHct>ctJepeH1.1HpyeMbl BOKpecTHOCTMTO'fKH Xo Mo6pa1.J.!aercH BHynb B3TOM TO'IKe: j{x0) = <p(x0) = 0. nycTb cp'(x)¢0 BOKpeCTHOCTM TO'IKM x0• EcnH cyll!eCTByer npeAen lim 1:ix~ =I, X-+X~ <p X (npe,D,en OTHOW8Hl1H /J.BYX 6eCKOH81/HO M8flb/X pa- BeH npe,D,eny OTHOW8Hl1H ux npOl13BOl/HblX, ecnu nocne,D,HUM cyw,ecrayer) npaBHnO nonMTanH, npH oo/oo. nyCTb ctJyHKl.IHH.f(x) Hcp(x) HenpepblBHbl HAMctJ- ctJepeHl.IHPYeMbl BOKpeCTHOCTH TO'fKH Xo (KPOMe TO'fKH Xo), B3TOM OKpeCTHOCTH lim/(x) = lim<p(x)= oo , <p'(x)=t:O. .r->xo .r-+.to j "'( ) EcnH cyl.J.!eCTByer npeAen lim ,(x) = l, x-+xo <p X TO Jim f (x) = lim f'(x) =I X-+Xo cp(x) X->Xo cp 1 (X) •TO lim f (x) = lim f:(x) = l X-+Xo <p(x) X-+Xo <p (x) np111M8Hll1M K cpyHKL.1111S1Mf(x) 111 cp(x) TeopeMy Kow1i1 ,[11151 OTP83Ka [xo;x], J18)Kall!ero B OKpeCTHOCTll1 T0'-1- j'(x)- f (x0 ) f'(c) Heonpe,[18118HHOCT!i1 8111,[la O·oo; 00-00; I'"; 00°; 0°CBO- ,[IS1TC51 K ABYM OCHOBHblM. no np!i13HaKy 0 CYLl.8CTBOBaH!i11i1 npe,Qenos: !~~+ ~)x= e CneACTBHS1 BToporo aaMe'larenbHoro npeAena lim loga(l + x) = 1 (a >O, 0¢1), B YaCTHOCT!il lim ln(~+x) = 1. x-+0 x ln a x-+0 lim a";1 =Ina x->0 (a>O), B '-laCTHOCTll1 Jim ex;l = 1. x->0 Kll1 Xo, TOr,[la ( ) ( ) = '( ) J <p X - <p x0 <p C r,Qe c 118)K!i1T M8)KAY x0 Iii x. - - - - l l lfll//llllWl/1/1/1/flll///ll • J/lllllljlllllfl/fl/lllf1t1/lllfllllllllffllllllilllllll711t---~ Xo C X np111 x - x0 B8J1111Yll1Ha c TaK)K8 CTp8Mll1TCS1 Kx0; nepel-1,QeM B npe,D,blAYll!8M paseHCTBe K npe,Qeny: 1 . f(x) _ li /'(c) !ID ( ) - m '( ) .X-+Xo cp x C-+Xo cp c TaK KaK Jim f'(x) = l TO lim /'(c) = I x-+xo cp'(x) c-+x0 cp'(c) no3TOMY Jim f (x) = l x- >x0 q> (x) Hanp1i1Mep, O·oo nycTbf(x)-0, cp(x)-oo npll1 x - x0• lim(/(x)·cp(x))=[O·oo]= lim f(x) =( 0 0] X-)>Xo X-+Xo 1 cp(x) lr'1HcJ>opMa'"'~OHHO-cnpaBO"IHast Ta611~'-'a -----© 000 «lllHcponnacT», 2006 r. 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  • 7.
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"' He33BMCHMOCTb CMC- Yll1CJ10 /1 Ha3blBalOTpa3M8p- nycTb 3Tlll AB8 On8palllllll TeMbl BeKTOPOB HOCTblO npocrpaHCTBa. nOAYlllHRIOTCR aKCll10MaM: 1.x+y=y+,Y; 2. (x+y)+z=x+(y+z)= =x+y+z; 3. x+O=x; 4.x+(-x)=O; 5. l ·x=x; 6. a((3x)=f3(ax)=af3x; 7. a(x+;1)=ax+ay; 8.(a+(3)x=ax+(3x; V; ;c, y, z, ...E V MH0)!{8CTBO vc ABYMR one- pal111RM111, YAOB11ersopR10- L1.1e8 aKCll10MaM Ha3blBaeTCR JlMHeMHblM npocrpaHCTBOM. 3neMeHTbl 11111HeC1Horo npo- crpaHcrsa Ha3b10aiorcR 0eK- ropaM111, o6o3HaYalOT- nycTb 111M88TCR /1 B8KTO- .... .... .... poB: X1, X2, •.. Xn. Cocra0111M 11111HeC1Hyio KOM- 6111HaL111110: a.,.Xi +a.2X2+ ... +a.llX,I = y. y=O, ec.n111 a1=~=...=a,,=O ~ Cll1CTeMa n B8KTOPOB - J1111HeC1H0-3aBll1Cll1Ma. Ecn11 cpeAM /1 seKTopos Ka- K11e-To k fll1Hei1H0-3aBl1Cl1- Mbl, TO BCH Cl1CTeMa BeKTO- poB HBnHeTCH fll1Hei1H0-3a- Bl1CUMOM. 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BeKTOPHOe npOM3BeAeHMe BeKTOpoa M ero CBOMCTB3 Tp111 HeKOMn.naHapHblX BBKTOpa o6pa3ylOT npasyJO Tpoi1Ky ec11111 c KOHL.la rperbero nosopor or nepsoro BeKTOpa KO BTOPOMYcosepwaeTCR npOTll1Byacosoc:i crpe11K111. Ec11111 no Yacosoc:i - ro nesyJO. CBOMCTBa: 1. (axlJ) =-(bx£:); 2. ;..,(axb')=(A.a)xb=ax(;..,"b); ... .... BeKTOPHblM npOM3BeAeHMeM BeKropa a Ha BeKTOP b 3. aJib «> (ax~=O;... -Ha3blBaeTCR BeKTOP c' KOTOPblll1: .... .... 1. nepneHAlllKYllRpeH BeKTOpaM a 111 b. (-+ "':'tl -+ -+ -+ ~ ~ 4. i....a+bjxc=axc+bxc . 2. lt1Meer AJ1111HY, YlllCJleHHO paBHYIO nllOLl.la,D,111 napanne- .... .... kl J.... .... axb= ax aY a, ........ norpaMMa, o6pa3osaHHoro Ha seKropax a 111 b. 12l=lal·lbl·sincp,rp,e cp=(a, b) bx by b, ........... 3. BeKTOpbl a ' b 111 c o6pa3ylOT npasylO rpoC1Ky BBKTOPOB. 6. CMewaHHOe npOM3BeAeHMe BeKTOPOB M ero CBOMCTBa CMewaHHOe npo1113sep,eH111e 3an1-1cb1sa10r s Bll1Ae: Id = (lixb)·cj. CMb1c.n CMeweHHoro npo1113se.a,eH111R: cHa- Yana ,D,Ba BeKropa BeKTOPHO nepeMHO)Ka- IOT, a 3areM no11yYeHHb1C1 cKanRpHo nepe- MHO)!{alOT c rpeTbl!1M BeKTOPOM. CMeWaH- HOe npovi30ep,eH111e npe.a,cras.nRer co6oC1 Yll1CJ10 - Yll1CJ10. Pe3yJlbTaT CMewaHHOfO npo1113seAeH1t15l - o6beM napa1111e11en111ne- p,a, o6pa30BaHHOf0 B8KTopaMll1. CBOMCTBa: 1. CM8WaHHoe npOll13B8,D,8Hll1e He MBHReTC5l np111 L111KJ1111Y8CKOC1 nepecraHOBKe COMHO- -> ' -+ -+ '"!") --. -4 -> ~ )!{1!1TeneC1: (axb)·c =(cxb)·a =(cxa)·b 2. CMewaHHoe npo1113sep,eH111e He 1113Me- Hll1TCR np111 nepeMeHe MecraM111 seKrop- HOfO Ill CKaJ15lpHoro npOlt13B8A8Hll1R: -) "":+ -+ .... --:+ -+ (axb)·a = a·( bxc) 3. CMewaHHoe npo1113se- .a,eH111e MeHReT 3HaK np111 nepeMeHe Meer Jll06blX ABYX BBKTO- poB-COMHQ)!{ll1TeJ18C1: -+ ~~ -->-+-=-> a·b·c =- a·c·b -t~-+ ->-> -+ a·b·c=-c·b·a 4. CM8WaHHoe npo1113se.a,eH1118 rpex HeHyne- BblX BeKTOPOB paBHO HYJllO rorp,a 111 TOJlb- KO rorp,a, KOfAa OHll1 KOMnJlaHapHbl. 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B 3TOM npocrpaHcrse ssep,eMell.le op,Hy onepaL111110. 0Ha 6yp,er y.a,00118- rsopRTb CJlB,D,YIOL1.1111M aKCll10MaM: 1. (x;y)=(y;x); 2. (x+Y; z)=(x;y)+(y; z); 3. (A.x;y) = A(x; y); 4. (x; x)= (x 2 ) 2: 0. YKa3aHHaR onepal111R Ha3b1Ba8TCR CKanRpHblM npOll13BBABHlt18M B8KTOpOB. N - MepH08 n111Hei;1Hoe npocrpaHCTBO c BBeAeHHOC1 onepaL1111ei;l CKaJ15lPHOfO npOlll3BBAe- H111R, Ha3b1Ba8TCR EBKJlMAOBblM npocrpaHCTBOM. /JflUHOM BBKTOpa Ha3blBaeTCR ap111Q>Me- TV1YeCKOe 3HaYeH111e KBaAparHoro KOPHR 111 cKansipHoro KBaApara: lxl=~(x 2 ). A11111Ha seKropa yp,osnersopRer cneAYIOLl.llllMyc.no0111RM: (x;y) s xY 1. 1112:0, ec.n111 lxl=O => x=O; I-+ ...I 2. 1;..,11=1;..,1.1.x1; 1:i~IY1<1 3. (x;J9<lxl·l.YI-HepaseHcrso Kow111-6yHRKoscKoro Ix·:, l.t;-YI ~ cos<p =Ix!·I.YI I.... -+I 1....11-+I -1< ,y <i4. x+y s x + y - HepaseHcrso rpeyro11bH1t1Ka -IXJ·I.YI- 7. nMHeMHble npeo6pa30B3HMSI npocTpaHCTBa. MaTpMQ3 nHHeMHOro npeo6pa30B3HMSI. CBSl3b MeJKAY KOOPAMH3T3MM 06pa3a M npoo6pa3a PaccMorp111M 11111HeC1Hoe npocrpaHcrso v, 6a3111c (e) 8 6a3111c (e'). BKOTOPOM Ka)K.QOMY 3neMeHTY X , Bc111.ny HeKoroporo 3aKoHa nocrasneH 3.neMeHT 3Toro )!{8 npocrpaHcrsa. .... /... .... Ji-+) -+x-'7y «> y = (x , rAe x - npoo6pa3, -+ y - o6pa3. Ka)K,D,OMY npoo6pa3y COOTBeTCTByer e.a,111HcrseHHb1C1 o6pa3. Ka)K.Qb1C1 06pa3 111Meer eA111HCTBBHHblC1 npoo6pa3. n111HeC1HOe npeo6pa30BaHll1e npocrpaHCT- Ba, np111 KOTOPOM CYLl.IBCTByer B3al!1MHOOA- H03HaYHbl8 COOTB8TCTBll1R. 6111eKT111sHoe npeo6pa3osaH111e Y=f(x) - Ha3b1Ba8TCR Jlll1HeC1HblM, ec11111 BblnOJ1HR- IOTC5l 2 YCJ10Bll1R: 1. F(x+y)=F(x) +F(Y); 2. F(A.x) = 'AF(x) . F(A. x+py) = 'AF(x )+PF(y') PaccMorp111M n-MepHoe n111HeC1Hoe npo- crpaHcrso (-+) ... -+ -+e :e1, e2 , ••• e,, -+ -) -+ .... x =x1e1+x2e2+ ... +xne11 AnR roro, YT06b1 3aAaTb 11111HeC1Hb1e npe- 06pa300aH111R B3TOM npocrpaHCTBe AOC- TaTOYHO 3a.a,aTb 3TO npeo6pa30BaH111e AJlR 6a3111CHblX BBKTOPOB. 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  • 8.
    8. CBH3b Ne)l(AyKOOPAMRara M OAHOro HToro )Ke 11MHeHHOro oneparopa s pa3HblX 6a3Hcax (;)4 (i) J=J<x) (e) (e") A I B I y = x y = x B = r-1 AT T- MaTp1i11..1a nepe- XOAa OT e K e', TO: x =Tx' y =Ty' Ax=ATx' Ty'=ATx' y'=T-'ATx' I B I y= x Ecn1-1 n 1.1HelilHbllil onepaTop 1.1MeeT B 6a- 31-1ce H9Bblp0)t(A9HHYIO MaTp1.11..1y T, MaT- p1.11..1a 3Toro onepaTopa B n1060M gpyroM 6a31.1ce He 6YABT BblpO)t(AeHa. 11 . Yron Me>KAY npAMOM MnnocKOCTblO. PaccTOAHMe OT TO'IKM AO nnOCKOCTM 6.: Ax+Bv+Cz+D=O - X- X y - v z- z npRMafl L: m 0 = n" 0 = p 0 nycTb cp - yron Me)t(AY nnocKOCTblO Iii npHMOlil. TorAa e- yron Me)t(AY -+ -+ n(A;B;C) 1.1 S(m;n;p), .... -+ e n·S ~ cos = 1-1liil· s HalilAeM sin cp, ecn1-1 <p$;-~" sin<p = sin~-e)= cose, T.K. sincpC?: O PaCCTOHHMe OT TO'fKMAO nJlOCKOCTM AaHo: 6.:Ax+By+ Cz+D=O PaccTORHl.'19 cl OT TOYKL-1 MoAO nnoCKO- CTl-1 6. pasHo MOAY!llO npoeKL.1-11.'1 seKTO- pa M0 M.. (rge M1(x1;y1;z1) - npol-13BO!lb- HaR TOYKa nnOCKOCTL-1) Ha HanpasneH1.1e HOpMaJlbHOro BSKTopa ii = (A; B; C). I M1M0 ·n d = npii M1Mo = liil = _ l(xo-x,)A+(yo-Y1)B+(zo-z1)I_ - .JA2+B2+C2 - Ax0+By0 +Cz0- Ax0- By0-Cz0 - .JA2+B2+c2 d = Ax0+By0+Cz0+D .JA2+B2+c2 Ecn1.1 nnocKOCTb 3agaHa ypasHeH1.1eM: X ·COSa +y ·cos p+z ·cosy - p =O' TO pacCTOSlHi.18 AO nJlOCKOCTV1 HaXOAV1TC51 no ¢opMyne: Id= lx ·cosa +y ·cos P+ z ·cosy -p 1I 9. lapai-repJCCTII ec1toe ypaa e e e- oro o epa1opa. Co6cTBelfHble senopbt nMHei4eoro oaeparopa M111:x csoicrsa I ECJ1V1 B 6a3.1C6 e Jl.1H61i1Hbllil onepaTOp .1M69T MaTpHLY .-1, a B 6a3.1C6 { e) onepaTop HMeeT MaTPVll.Y B, ~ det(A- A.E)= det(B- A.£), A. - npOV13BO!lbHOe Y1t1cno ;o! 0, E - 9AV1HV1YHafl MaTp1i11..1a. det(B-A.E) =det(T-1AT-A.T-'ET)= =det(T-' (A - A.E)T)= det r -1 det(A+A.X); detT=detA- 1 = delA 1 0 ... 0 a11-A. a12 ... a1,, az1 az2-A ..· az,, ... a,,1 a,,2... a,,,, 0 0 ... 1 ECJlV1 xapaKTepV1CTV1Y6CKV1 MHOrOYneH J1 V1H6i:1Horo onepaTopa np1t1pOBHSlTb K O, nonyYVIM xapaKTep1t1cT1t1YecKoe ypasHeH1t1e Jl1t1Hei:1Horo onepaTopa. Co6cTeeHHbte eeKTOpbt JlMHeMHoro onepaTcipa HeHynesolil BBKTOP xHa3blBa6TCSl co6CTB6HHblM BBKTOPOM JlV1HelilHoro onepaTopa, ecn1i1 AX=k X onepaTop K x, nonyY1t1M 3TOT )!(9 x, yMH0- )!(6HHbli:i Ha HeKOTopoe k. k - co6cTBeHHoe Y1t1cno onepaTopa A=(; ~) -+ (2 1] ( I) l ll -+ Ax = 3 0)' - 3 = (- l)·c-3)= - x 12. noeepxHOCTM eroporo nopRAKa OnpeAeneHMe:YpasHeH1i1e B1t1Aa a11x2 +2a,2xy+2a22y2 +2auxz+2a23yz+a33 z 2 +2a14x+2ai4y+2a31 z+a44 =0, rAe aij(i,j = 1...11) A6t1CTBV1T6J1bHble 'iVICJla, Ha3blBaeTCSl 06ll.1"1M ypaBH6Hlt1- eM nosepxHOCTV1 BToporo nopRAKa. B 3aBl-1CV1MOCT"1 OT napaMeTpa a~ nonyYalOTCSl CJ16AYIOll.IV16 KJ1aCCV1Y6- CKV1e noaepXHOCTV1 (BCe napaMeTpbl nOJ10)t(lt1T6JlbHbl6 Ylt1CJ1a): 2 y2 z2 x2 +-b2 +1=1- rpexocHblM :Jnnuncou,a; a c x2 y 2 z2 ~+ -b2 -2=1- o,aHononocHblM runep6onou,a; a c 2 y2 z2 x2 +-b2 -2 =-1 -,asynonocTHblM r11nep6ono11,a; a c 2 y2 z2 x, +-b2 -2=0 - KoHyc sroporo nopHfJ.Ka; a- c 2 2 ; 2 +}i-= 2z - ann11nr111./eCK11i1 napa6ono11.a; 2 2 ; 2 - ~2 = 2z - r11nep6onu'leCKMM napa6onou/l,; x 2 +y 2 +z 2 =0 - TOl./KM. 2 2 ?+ti-=1 - 3flfll1nTl11./8CKUM L/MflMH/l,p,' x2 y2 a2- b2= I - r11nep6on111./ecK11i1 qun11H,ap; q2 =2ax - napa6onul./eCKl1MLJMflUH/l,p; a2 x2 - b2 y2 =0- napa nepeceKa10~11xcH nnocKocreill; x2 - a2 = 0 - napa napannenbHblX nnocKocreu; x2 +y2 = 0 - npHMaH. Bee yKa3aHHble ypasHeH1t1fl Ha3b1Ba10TCfl KaHOH1t1YecK1t1M1-1. OCHOBHblM M6TOAOM V13YY6Hlt1Sl nosepXHOCTelil BToporo nopS!gKa - M6TOA ceYeHVllil, KOTOpbllil COCTOVIT B nocTpoeHV1V1 J1V1HV1iil (CeY6HV1i:i) gaHHblX nllOCKOCTelil B YaCTHOCTV1 c nnocKOCTSlMV1, napannenbHblMV1 KOOPAlt1HaT- HblM nnOCKOCT51M. 10. fiJJOCKOCTb BnpDCTpaHCTBe. BMAbl ypaseeHMA nnoc1oc1ei4. Vron MeJKAy nnocKOCTAMM YpaeHeHMe nnocKOCTM, npoxoAHIJ.leM 'fepe3 33A3HHYtO TO'fKy, nepneHAMKYllHPHO A3HHOMY eeKTOPY nycTb nllOCKOCTb 3agaHa TOYKOlil M0 (x0 ;y0;z0) V1 BeKTO- pOM n(A;B;C)' nepneHAl-1KYllflPHOlil 3TOVI nJlOCKOCTl-1. 803bM9M npOl-13BOJlbHYIO TO'iKY M(x;y; z) 1-1 COCTaBl-1M B9KTOp M0M., = (x-x0 ; y-y0; z-z0). np1-1 Jll060M pacno- Jl0)!(8HV1V1 TOYKl-1 M Ha nJlOCKOCTl-1 Q rtJ_ MoM . n03TO- MY ti·M0M = 0. A (x-x0)+B(y-y0)+C(z-z0)=0 0611.1ee ypaeHeHMe nJlOCKOCTM 6.: Ax+By+Cz+D=O • Ecn1-1 D=O, TO gaHHOMY ypaBHeH1t110 YAOBneTsopReT TOYKa 0(0;0;0). • ECJll-1 C=OTO BSKTOp n(A;B;O).loz. CJ18AOBaTeJlbHO, nnOCKOCTb napanJlSJlbHa OCV1 oz, ec111-1 B=O - TO oy, 6CJ1V1 A= 0 - TO ox. • ECJ1V1 C=D=O, TO nnOCKOCTb npOXOAl-1T Yepe3 0(0;O;0), napannenbHO oc1.1 oz. AHanor1t1YHO np1-1 A=D=O1-1 B=D=O. • ECJll-1 A=B=O, TO ypaBH6HV1e npL'1M6T BL'1A Z=-@ nnocKOCTb napannenbHa nnocKocr 1i1 OxJ'· • ECJ1V1 A=B=D=O, TO ypaBH6HV1e l-1M66T BL'1)J, z=O. 3To ypaBHeH1t1e nnocKOCTV1 Oxy . YpaeHeHMe nnocKOCTM, npoxoAHIJ.leM 'fepe3 TPM TO'fKM 803bMeM Ha nllOCKOCTV1 TOYKY P(x;y;z). CocTaB1t1M seKTOpb1: ---+ KP=(x- x,; y-y,; z- z1) KM=(x2-x,; y2-y,; z2-z1) KJi!=~r.3-x1; y3-y,; Z3- z,) 3TV1 B9KTOpbl Jle)t(aT B OP,HOi:i nJlOCKOCTV1, cnegoBaTe!lb- HO OHV1 KOMnJlaHapHbl: y - y, z- z1 ) 12-Y1 Z2- Z1 = 0 Y3-Y1 Z3-Z1 YpaeHeHMe nnocKOCTM e oTpe3Kax nycTb nllOCKOCTb OTCeKaeT Ha OCSlX OTp93KV1, T.e. npoXOAVIT Yepe3 TOYK"1: A(a;O;O) B(O;b;O) C(O;O;c) x- a y z x y z 1 - a b 0 = 0 - +-b +-=a c -a 0 c HopManbHOe ypaeHeHMe nnocKOCTM Id= Ix.cosa. +y .cos p+ z .cosy - p 11 "1HcpOpMa1.4HOHHO-cnpaBOYHaS1 Ta6nH1.4a I • © 000 «V1Hc:j:lon11acT», 2006 •I . . r. MocKsa, Kaw1-1pcKoe wocce, 21 -• • E-mail: mail@infoplast.ru, --• http://www.infoplast.ru •• •Ten.: (095) 320-94-89/88 ' Cl C• ~ LI'.... ='() "°'-...... ~ LI' : '() •......: '() •o ;,,._ 0 '() (t, -~ no.anHCaHO s ne'ISTb 30.03.06. THp8)K 4000 3K3. 3aKa3 N!/3106. "13.Qarenb 000 «"1H¢onnacr», MocKsa, KawupcKoe wocce, 21. Twnorpa¢Hfl 000 •Busa-Crap». 107023, MocKsa, yn. 3fleKTfJ038BO.O.CKaR, 20.
  • 9.
    f?ll ·rr I'r.rr 1· r·rr>J. t..f..!..J_£!}_.r_ G ROOM i1m,1A11 KOMHA'llA - ' ..,,......,
  • 10.
    to wotch lw:i1ff to cry lkrnil ~ O&PAl 01JAii'1 E STREET/YJlHUA to depart to arrive (Ji"pa:I! to wait fweil) to fly (flai l to fp':rplei (>' 1"11vl to skate l~kl'iiJ to cycle 1'•11ikll pedestrian cro11f'19 lpi ilc1i1r1:111 ~r ·.1111 nowexQAHt.ll:iMP••OA to talk [IJ:kj to go (lJ~UI to walk [wo:k] to cross fkrJ'( •
  • 11.
    BMHorpaA Mango I'm:r(l9••1 MaHro Coconut I ~oukonAll ~Ko•oc Tangerine I i:cnd,Jo"ri:n) Pear (prJ( ub ~ A J U H A H ~ E r; I 'frI . r.rr i · r· rrl,l ~r •->:JI _ FRUITS <DPYK'l.'hl Cherry I !fcril •BMWHJl Apple r..,.,,1 ll6no•o Pinapple I p:1111teplI Orange " r Jrin11l) ' AnenbCMH Pomegranate I 1"'11119rtcnill Raspberry I'rn:zboril M anHHa. Strawberry r<lr:>:b.>ril Kny6H11Ka Kiwi fruit I ' ~i:wi:l'ru:tl Avocado J,:CY;J. lt1;di'1U) Watermelon I w:.1ouadJn( KMBH "C/cwmi.15 Lemon I' k monl M elon rmelonJ AblHft nepCHK Apricot I <iprikJtI A6pl1KOC Banana lhJ no:noJ t.•
  • 12.
    HH4'0nAACT TM www.'infoplast.ru nyreBOAMTenbno "18CTHM pe"IM -------1'1Mff cyL11eCTBlr1TeJ1bHOe AHrn111i1cK111e cylljeCTB111Te11bHb1e AeflHTCH Ha: MMeHa Hap114aTenbHb1e: house, star, man MMeHa co6CTBeHHble: White House, Earth, John. B 111MeHax co6c TBeHHb1x (BKfllOYaH reorpa- cp1114ecK111e Ha3BaH111H , 3arna0111H , Ha3BaH111H yY- pell<AeH111H 111 T.n .), COCTOHUjll1X 6011ee YeM 1113 OAHOro CflOBa, see CflOBa n111wyTCH c 3arnaB- HOH 6yKBbl. CyUjeCTB111Te!lbHb1e 6b10a10r 11c'!11cnS1eMb1e: a table, a town He11c'!11cnS1eMb1e: sugar, honesty l11aro11 , OTHOCHUjll1HCH K Hell1C4111C!lHeMOMY cylljeCTBll1Te!lbHOMy, scerAa CTOll1T B eA111HCT- BeHHOM 4111Cfle. Water passes under the bridge. Her hair is black. He111cY111c11HeMb1e cylljeCTB111Te!lbHb1e H111- KOrAa He ynoTpe6!1HIOTCH c HeonpeAe!leHHblM aprnKneM a/an . Cnosa, o603Ha4al0Ujll1e KO!lll14eCTBO, CTO- HT nepeA cylljeCTBll1Te!lbHblM . ,Qm1 MC'lMCnSleMblX cy14ecTBMTenbHblX: 0A111H One table Kall<AblH each/every table ,[lsa/o6a/napa two/both/a couple of tables Tp111 111 T.A. three etc. tables HecKO!lbKO a few/several tables MHoro Mano many/a number of tables few tables ,QnSI HeMC'lMCnSleMblX cy14ecTBMTenbHblX: HeMHoro a little sugar MHoro much sugar OYeHb MHOro a great deal of sugar Mano little sugar ,QnSI MC'lMCnSleMblX .. HeMC'lMCnSleMblX cy14eCTBMTenbHblX: HeT no tables, HeMHoro some sugar tables, sugar(HeKOTOpoe KO!lll14eCTBO) MHoro a Jot of/Jots of tables, !plenty of sugar 5onbwaH YaCTb most tables/sugar Bce/ secb 8HMM8HMe! Few - Mano Little - Mano all tables/sugar a few - HeMHOro (HeCKOflb- KO WTYK) a little - HeMHoro (HeKOTO- poe KOflll14eCTBO MHo>KeCTBeHHOe '!Meno cy14ecTBMTenbHblX 50!lbWll1HCTBO c ylljeCTBll1Te!lbHblX o6pa3y- e T MHOll<eCTBeHHOe 4111Cfl0 c nOMOUjblO OKOH- 4 a Hll1H -S. E c 11111 eA111HCTBeHHOe Y111c110 0 KaHY1110aeTCH Ha: S, sh, ch. X, z - np1116a0m:1eTCH OKOHYaHHe -es: classes, bushes, ditches. minxes. buzzes. 0 - np1116aa11HeTC5! OKOtNaM1e -s. es. ooiatoes. eroes. rnaCHblH + y - np1116aB11HeTCH OKOHYaH111e -s: toys, bays cornaCHblH + y , - y MeHHeTCH Hai 111 npH6aB- !1HeTCH OKOHYaH111e -es: babies, parties. BHMM8HMe! HCKfllO'leHMSI: EA.'!. MH.'l. Child children Foot feet Louse lice Man men Mouse mice Ox oxen Sheep sheep Tooth teeth Woman women HeKOTOpb1e cnosa Heattrn111HCKoro npo111c- XOll<AeHHH 111MelOT 3all1MCTBOBaHHble cpopMbl MHOll<eCTBeHHOro 4111CJla: EA.'!. MH.'l. Analysis analyses Appendix appendices, appendixes Bacterium bacteria Basis bases Crisis crises Criterion criteria Curriculum curricula Datum data Medium media Memorandum memoranda Oasis oases Phenomenon phenomena Stimulus stimuli Syllabus syllabuses, syllabi Vertebra vertebrae np11TS1>1<aTenbHb1iil naAe>K y aHrnll1HCKll1X cylljeCTBll1Te!lbHblX scero ABa n~ell<a - 061411iil 11 npMTSl>KaTenbHblM. np111rnll<aTeflbHblH naAelK 06pa3yeTCH C noMOll.blO OKOHYaH111H - 's AflH eA111HCTBeHHoro 4111C!la 111 -s' AflH MHOll<eCTBeHHOro. The boy's book Ho: The boys' books. Ec11111 CylljeCTBll1Te!lbHOe OKaH4111BaeTCH Ha s , TO B03M0)1(Hbl o6a 0ap111aHTa OKOHYaH111H: James's bag 111111 James' bag. ApntKllb OnpeAeneHHblM a pTMKnb (THE) OnpeAeneHHblH aprnKflb ynoTpe611HeTcH: - c 111C4111C!lHeMblMll1 cylljeCTBll1Te!lbHblMll1 B eA111HCTBeHHOM 111 MHOll<eCTBeHHOM 4HC!le, - C Hell1C4111C!lHeMblMll1 CylljeCTBHTe!lbHblMll1. THE ynoTpe6nS1eTCS1: - ec11111 npeAMeT H3BecTeH ro0opH1.4eMy: "'ie car I have s very 'ast ~e e who ere ay '19 'oott:Ja e - Ec11111 npeAMeT ynoM111Ha11cH paHee: Mary drank a glass of wine. Then she washed the glass and put it away. - EcnH npeAMeT eA111HCTBeHHblH B CBOeM po- Ae: The sky is blue. The sun is shining. - Ec11111 cylljeCTB111Te!lbHoe B eA111HCTBeHHOM 4111c11e npeACTaBnHeT 4e11b1H Knacc npeA- MeTOB: The average family now has a computer. The computer is a most important invention. - Ec11111 nepeA cylljeCTBll1TeflbHblM CT0111T np111- 11araTe!lbHOe B npeBOCXOAHOH CTeneH111: Theresa is the tallest girl in town. HeonpeAe n e HHblM apTMKflb (A/AN) HeonpeAeneHHblH aprnKflb ynoTpe611HeT- CH TO!lbKO c 111C4111C!lHeMblMll1 cylljeCTBll1Te!lb- HblMll1 B eA111HCTBeHHOM 4111Cne: a boy, a spring, a dictionary, a piece of chalk. CllopMa AN cTaB111TcH nepeA cylljecrn111- Te11bHb1M111, Ha4111Hal0Ujll1Mll1CH Ha rnaCHblH: an apple, an examination , an hour (Ho a universi- ty, a hotel). A/AN yno Tpe611S1eTCS1: - Ec11111 npeAMeT He11130ecrnH rosopHUjeMy: I have a car. Mary has a test tomorrow. - Ec11111 npeAMeT ynoM111HaeTcH 0nep0b1e: A banana is usually sweet. A book is a good friend on a long trip. OTCYTCTBMe apTMKflSI nepeA 111C4111C!lHeMblMll1 CylljeCTBll1TeflbHbl- Mll1 BO MHOll<eCTBeHHOM 4111C!le 111 Hell1C4111C!lHe- MblMll1 CylljeCTBll1Te!lbHblMll1 He CTaBll1TCH onpe- Ae!leHHblH apT111Kflb, KOrAa OHll1 o603 Ha4alOT secb Knacc npeAMeTOB. I like cherries. The cherries in this bag are ripe. Chinese grow rice. The rice I ate last night was good. BHMM8HMe! nepeA cylljeCTBll1Te!lbHblM B eA111HCTBeHHOM 4111C!le 06H3aTe!lbHO AO!lll<Hbl CTOHTb: - aprnK!lb (a book, the car, an uncle) 11111111 - yKa3aTenbHOe Mecrn111MeH111e (this TV, that radio, this book) 11111111 - np111rnll<aTe!lbHOe MeCTOll1MeH111e 11111111 c yllje- CTBll1Te!lbHOe B np111rnll<aTe!lbHOM naAell<e (my pencil, her key, Mary's room). MecT01r1MeH1r1ff n1114Hble MeCT0111MeHll1H 111MelOT AB8 naAe>Ka: 111MeHll1Te!lbHblH 111 06beKTHblH . "1MeH11Te11bHblM naAe>K (c11y>1<11T n0Ane>1<a1411M) I >1 You He, she, it We You They Tb / OH, OHa, OHO Mb / Bbl OHM BHM aHtte! ecT0111 eH111e you acerAa Tpe6y- e~ - aro a a cpopue o ecrne >;Oro Yl-!Cna.
  • 13.
    06beKTHblM n&Ae>K (cny>KMT AOnonHeHMeM) Me You Him,her, it Us You them npMTSl>K8Te/1bHble MeCTOMMeHMSI (0603H8"18IOT npMH8A/1e>KHOCTb) My, (mine) MOH Your (yours) rnoH His, her (hers), its ero, ee Our (ours) Haw Your (yours) saw Their (theirs) HX 8HMM8HMe! ct>opMbl B CK06Kax yn0Tpe611S110TCSI, KOrAa 3a MeCTOMMeHHeM He C11eAyeT onpeAe11sieMOe C110BO: This is my book. Ho: This book is mine. This is our room, and that is yours. Whose bag is it? - Hers. Bo3epaTHb1e MeCT0111MeH111si B aHmHHCKOM s:i3b1Ke Ka>KAOMY 11M4HOMY Mec- TOMMeHMIO COOTBeTCTByeT CBOe B03BpaTHOe: I- Myself You - yourself He, she, it- himself, herself, itself We - ourselves You - yourselves They- themselves 8HMM8HMe! B03BpaTHble MeCTOHMeHHSI MOryT HMeTb pa3- Hble 3Ha4eHHSI: «Ce6si» («Ce6e» H T.n.) 111111-1 «CaM » . Look at yourself! - nocMoTpH Ha ce6si! He is always pleased with himself. - OH scerAa AOB011eH co6oH. I like to drive myself. - 51 111061110 secT111 Maw1-1- HY caM. 6e3/1M"IHble MeCTOMMeHMSI One (s 3Ha4eHHH «mo6oc; 4e11oseK», «1110AH» B 4e110M) One should always be on time. You (s 3Ha4eHHH «111060H 4e11oseK», «1110AH» B 4e110M) I am lost: how do you get to the train station from here? They (B 3Ha4eHHH «HeKTO», «1110AH» B 4e110M. They say the weather will be warm in summer. - rosopsiT, 11ernM 6yAeT Ten110. . lllMfl np1,u1araTenbHoe np1-111araTe11bHble B aHf!lHHCKOM Sl3b1Ke CTOSIT nepeA onpeAe11SleMblM C110BOM. CTeneHM cpaeHeHMSI np11111araTe11bHblX. 0AHOC110:>t<Hb1e 1-1 ABYXC~O:>t<Hb1e np1-111araTe11b- Hb1e o6pa3ylOT CTeneHH cpaBHeHHSI c noMO- LlblO cycpcpMKCOB: - cpaBHMTe/lbHSSI CTeneHb: -er - npeBOCXOAH8SI CTeneHb: -est big - bigger - biggest; clever - cleverer - cleverest np11111araTe11bHble 6011ee 4eM 1-13 ABYX C110rDB- C nOMOLLblO C110B: - more - cpaeHMTe/lbHasi cTeneHb - the most - npeBOCXOAH8SI CTeneHb Beautiful - more beau ifu1 - the most bea Extravagan - ore exrravaga e mos extra ag L BH111MaH111e: nepeA np1-111araTe11bHblM B npe- BOCXOAHOH CTeneHH BCerAa CTOHT onpeAe- 11eHHblH aprnK11b. Earth is big. Uranus is bigger. Jupiter is the biggest of all planets. Nuclear physics is the most difficult subject of all. nocK011bKY aHmHHCKMe cyl.leCTBHTe11b- Hb1e He CK110HSllOTCS'I no nSAe:>KaM, cpyHK4MH nSAe:>KeH 6epyT Ha ce6si npeA11or111. npeA/lOr - 3TO c11y>1<e6H8SI "18CTb pe"IM, nOK83blB8IOll.l8SI cne4111cp1111.1ecKMe OTHOWe- HMSI Me>KAY ABYMSI npeAMeTSMM. Cyl.leCTBMTe11bHb1e c npeA110raM1-1 OTBe4alOT Ha BOnpOCbl «fAe?», «KOfAa?», «KaK?», a TaK>Ke Ha naAe>KHble BOnpOCbl. The boys are in the yard («r!Je?») Mary is coming by train («KaK? ») We leave at5.00 p.m. («KOr!JB? ») I gave the book to my brother («KoMy? ») The children are drawing on the pavement («Ha YeM? ») with chalk («YeM? ») Ha1116011ee ynoTpe6111Te11bHb1e npeA11or111 about above across after against along among around at before behind below beneath beside between beyond by despite down during for Ill MX OCHOBHble 3H8"1eHMSI: o; BOKpyr HaA nonepeK; HanpoTMB noc11e nporns BA011b cpeAH BOKpyr y, OK0110 nepeA 3a nOA noA OK0110 Me>KAY noA; 3a y, npH, OK0110 HeCMOTpSI Ha BHM3 BO BpeMSI A11S1 from oT, 1113 in(tb} B like C110BHO near so311e Of OT off yKa3blBaeT Ha OTAMeHHe OT 4ero-11. on Ha out 1113 (OTAa11eHHe, ABH:>KeHHe Hapy:>t<y) over through throughout till to(ward)(s) under HaA CKB03b (Ha)CKB03b AO (speMs:i) K (Hanpas11eH1-1e) noA until up upon AO (speMsi) yKa3blBaeT Ha ABM>KeHHe BBepx Ha with within without c B (npeAe11ax) 6e3 BHMM8HMe! Ka:>KAblH aHf!lMHCKHH npeA110f HMeeT HeCK011bKO (11111111 MHOro) 3Ha4eHHH Ill c11y4aes ynoTpe611eH111s:i. Ha aonpocb1 Koro? Yero? KoMy? YeMY? 0 OrneYalOr cy~. c npe!JI10fBM/lf of, from to with HapeY111e MHorne Hape4HSI o6pa3ylOTCSI OT np1-111a- raTe11bHblX c nOMOLLblO cycpcpMKCa -ly (quick- ly, naturally, beautifully, largely etc.). He spoke quickly (quick+ly) She opened the box very carefully (careful+ly). Hape"IMSI "18CTO OTBe"ISIOT HS eonpOCbl: KaK? She opens the present quickly. rAe? She opens the present inside. KorAa? She opened the present yesterday. B KSKOM cTeneH111? She opened the present very quickly. Hape"IMSI MOryT 03H8"18Tb: - speMs:i (tomorrow, yesterday, today, early, late, etc.) John arrives tomorrow - 4aCTOTY cosepweHMSI AeHCTBHSI (some- times, usually, often, never etc.). How often do you smoke? - I never smoke. 100% < = > 50% => <=> 0% always usually sometimes rarely never often occasionally seldom hardly ever not ever Hape4HSI, o603Ha4al0LlHe speMs:i CTOSIT B Ha- 4a11e 1-111111 B KOH4e npeAf10>KeHHSI. I saw my friend yesterday. Tomorrow we shall go to the library. Hape41-1si, o6o3Ha4al0LlHe 4acT0Ty cosepwe- HHSI AeHCTBMSI, CTOSIT - nepeA maro110M B npocTblX speMeHax: usu- ally comes, never ate, often do, never had She usually comes at 8 p.m. - noc11e maro11a to be B npocTblX speMeHax: is usually, are never, was often, were rarely She is usually on time. Me>KAY BCnOMOraTe11bHblM HOCHOBHblM maro- 110M B c11o:>t<Hb1x speMeHax: has always been, will never eat, had often come. She has always been on time. CTeneHM cpaeHeHMSI Hape1.1Mi4 Hape4111si 06pa3y10T cTeneHH cpasHeHMSI TaK >Ke, KaK np1-111araTe11bHb1e. Hape4HSI Me- Hee 4eM H3 ABYX c11oros - c noMOLLblO cycpcp1-1- Kcos: -er (cpaBHHTe11bHasi crnneHb) -est (npesocxOAHasi crnneHb) late - later - latest early - earlier - earliest. Hape4HSI, COCTOSILLHe 6011ee 4eM 1-13 ABYX C110rDB, a TaK>Ke 6011bWHHCTBO Hape4HH Ha - ly, o6pa30BaHHblX OT np1-111araTe11bHblX, - c noMOLLblO C110B: - more (cpaBHHTe11bHas:i cTeneHb) - most (npeBOCXOAHas:i CTeneHb) quickly - more quickly - most quickly intensely - more intensely - most intensely BHMM8HMe! lllCK/llO"leHMSI: Well - better - best Badly - worse - worst Much - more - most Little - less - least /lfH¢opMaljJ10HHO-cnpaao4HilR ra6nuqa C 000 •/lfH¢onnacr•,2004 r MocKBll, KawHpcKoe wocce, 21 E- ma&111/oplastIU ....,..n/oplast.IU
  • 14.
    HH4'0nlACT ™ www.infoplast.ru AHrmticKMirnaron <l>opMbl, epeMeHa, 3anorn AHrm1i;CKi.1i; rnaron i.'!MeeT Tpi.1 OCHOBHblX cpopMbl: 1 - HeonpeAelleHHaJI <1>opMa 2 - npoWeAWee BpeMSI 3 - np11'iaCTlle npoweAWero epeMeHll (np11'iacT11e II) 2 3 Stay stayed stayed Want wanted wanted Look looked looked Study studied studied npae1-111bHb1e rnaro11b1 o6pa3ytoT eTopyto "' TpeTbto cpopMbl c noMOl.11bto cycpcp1-1Kca -ed. 50J1bWi.1HCTBO aHrni.'li;CKi.'IX rnaronoe npaBi.'!Jlb- Hble. YeTeeprnR cpopMa rnarona 06pa3yeTCR c no- MOl.11bto cycpcpi.1KCa -ing («i.1HroBaR» cpopMa) «111HroeaR» cpopMa MO:>KeT RBJlRTbCR: - np1-14acrneM HaCTORl.11ero epeMeHi.1 (np1-1- 4acrneM I) · - repyHAi.'leM. np1-14acrne HaCTORl.11ero epeMeHi.1 CllY:>Ki.'IT B npeAJlO)l(eHi.'li.1 onpeAeJleHi.'leM: a playing boy, a rolling stone, a dancing girl. EAi.1Hi.14HOe np1-14acrne CTOi.'IT nepeA onpeAe- JlReMblM CJlOBOM. np1-14acrne, BXOARl.11ee B np1-1YaCTHb1i; o6opoT, CTOi.'IT nocne onpeAellR- eMoro cnoea: a boy playing football, a stone rolling down, a girl dancing salsa. fepyHAi.'li; BblnOJlHReT T8 :>Ke cpyHK4i.1i.1, 4TO i.1 cy1.11ecTBi.1T8JlbHOe. Walking is a good exercise (nOAJ1e:>Ka1.11ee). We enjoy playing tennis (Aono11HeH1-1e). B Ka4eCTee AOno11HeHi.1R repyHAi.'li; ynoTpe6- JlReTcR nocne onpeAeJleHHblX rnaronoe: Appreciate Avoid Consider (think aboulj Discuss (talk aboulj Enjoy Finish (get through) Keep (keep on) Quit(give up) Suggest Hanp1-1Mep: He quits smoking. Avoid making mistakes! repyHA"'i; l'IMeeT Aei;cTBl'ITe11bHb1i; "' cTpaAa- Te11bHb1i; 3anorn, HaCTORl.11ee "' npoweAWee epeMeHa. fepyHAllH B CTpaAaTellbHOM 3a11ore (Passive Gerund): Being+ I appreciate being npi.14acrne II invited to this event repyHAMH e npoweAweM epeMeH11 (Past Gerund): Having + npw-iacTI1e II I appreciate havrng had the opportunity to eet her. fepyHAllH B CTpaAaTellbHOM 3a11ore npoweAwero epeMeH11 (Past-Passive Gerund): Having been + I appreciate having been np1-14acrne II told the news. Cnpsut<eH1t1e rnarona to be To be BblCTynaeT KaK: a) ecnoMorarn11bHb1i; rnaron npi.1 o6pa3oeaHi.1i.1 cpopM Continuous "' Passive 6) rnaron-CBR3Ka B COCTaBHOM l'IMeHHOM CKa- 3yeMOM: He is a teacher HacTOSIUee npoweAwee liYAYUee epeMsi epeMsi epeMsi I am I was I will (shallj be You are You were You will be He, she, it is He, she, it was He, she, it will be We are We were We will (shallj be They are They were They will be BpeMeHa rnarona npocToe HaCTOSIUee (Simple Present, Present Indefinite) npocrne HaCTORl.11ee epeMR o6o3Ha4aeT npi.1- Bbl4Hoe Aei;cTBl'le: TO, 4TO YenoeeK AenaeT Ka:>KAbli; AeHb (HeAento, M8CR4, roA "' T.n.). Children go to school every day. B TpeTbeM 11i.14e eAl'IHCTBeHHoro 4i.1Cna rnaron e Present Indefinite npl'IHl'IMaeT OKOH4aHi.1e -s. Bo ecex OCTaJlbHblX 1li.14ax "' 4i.1Cflax COBnaAa- eT c HeonpeAeJleHHOi; cpopMOi;. I eat, study You eat, study He, she, it eats, studies We eat, study They eat, study BH11MaH11e! One person eats. Two persons eat. One dog barks. Many dogs bark. HacTOSIUee npOAOll>KeHHoe (Present Continuous, Present Progressive) 06pa3yeTCR c noMOl.11bto rnarona to be e Jli.14- Hoi; cpopMe HaCTORl.ljero epeMeHi.1 + np11'iac- T11e I CMb1c11oeoro r11aro11a . 03Ha4aeT Aei;CTBl'le, npOl'ICXOARl.ljee B HaCTO- Rlljl'li; MOMeHT, T.e. B MOMeHT roeopeHl'IR. What are you doing now? I am eating now, at present You are eating He, she. it 1s eatJng Weareeatmg T. ey are ea ng Btt11MaH11e! B npoAon:>KeHHoi; cpopMe He ynoTpe611RtoTCR rnaro11b1: Be Believe Belong Exist Forget Hate Have (B 3Ha4eHl'li.1 «l'IMeTb») Hear Love Need Own Possess Prefer Remember See Think Know Like (e 3Ha4eHi.1i.1 «nonaraTb" ) Understand Want npocTOe npoweAwee (Simple Past, Past Indefinite) 06pa3yeTCR c nOMOl.11blO cycpcpi.1KCa -ed. 03Ha4aeT 3aKOH4eHHoe l'lni.1 npi.1Bbl4Hoe Aei;- CTBl'le B npOWJlOM. YacTO l'IMeeT npi.1 ce6e o6- CTOSIT8JlbCTBa epeMeHl'I: yesterday, last week (month), a year ago etc. What did you do yesterday? I cooked, studied You cooked, studied He, she, it cooked, studied yesterday, last week etc. We cooked, studied They cooked, studied npoweAwee npOAOll>KeHHOe (Past Continuous, Past Progressive) 06pa3yeTCR c noMOl.ljbto rnarona to be e npo- WSAWeM epeMeHl'I + np11'1aCTlle I CMblCllO- eoro rnaro11a. 03Ha4aeT Aei;cTBl'le, Alll'leweecR e onpeAe- 11eHHb1i; MOMeHT B npOWJlOM i.1111'1 OAHOBpe- MeHHO c APYrnM Aei;crnl'!eM e npownoM. What were you doing yesterday at 5 o'clock? What was she doing when you knocked the door? I was reading You were reading yesterday at 5 o 'clock; when someone knocked the door. He, she, it was reading We were reading They were reading npocTOe 6YAYUee (Simple Future, Future Indefinite) 06pa3yeTCR c noMOl.ljbto ecnoMoraTeJlbHOro rnarona will (AllR nepeoro 11i.14a B03MO:>KeH rnaron shall) + llH<l>llHllTllB CMblCllOBOro rnaro11a. 03Ha4aeT 3an11aHi.1poeaHHoe Aei;cTBl'le e 6y- AYLl18M (rnni.14Hb1e 06cTORT8JlbCTea epeMeHi.1: tomorrow, next week, next month etc.) What will you do tomorrow? I will (shallj work You will work He, she, it will work tomorrow; in the evening We will (shall) work in the evening. They will work
  • 15.
    6yAy~ee npOAOmKeHHoe (Future Continuous,Future Progressive) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona will (AJll'I nepBoro n1114a B03MO>KeH rnaron shall) + be + «MHroeaJI» ci>opMa CMbl- cnoeoro rnarona. 03Ha4aeT AnlllTenbHoe AeHCTBllle, KOTopoe 6yAeT npOlllCXOAlllTb B 6YAYlJ.1eM n11160 Haxo- AlllTbCS'I Bnpo4ecce BonpeAeneHHblH MOMeHT B 6YAYlJ.1eM. What wilt you be doing at 5 o'clock tomor- row'? I will (shallj be working You wilt be working at 5 o'clock tomorrow. He, she, it will be working We wilt (shalt) be working HacTOR~ coeepweHHoe (Present Perfect) 06pa3yeTCS'I c noMOlJ.1blO BcnoMoraTenbHoro rnarona have B n1114HOH cj:JopMe HacTOS'llJ.1ero BpeMeHlll + Participle II CMb1cnoeoro rnaro- na. 03Ha4aeT: a) AeHCTBllle, Ha4aBweecs:1 BnpownoM 111 He 3aBepweHHoe K MOMeHTY roBopeH111s:1 (Durative Perfect): I have worked since 5 o'clock (and I am still working now). 6) coBepweHHoe B npownoM AeHCTBllle, pe3ynbTaT KOTOporo CKa3blBaeTCS'I B HaCTOS'l- lJ.1eM (Resultative Perfect): I have packed my things (so they are in the suitcase now). I have worked You have worked He, she, it, has worked We have worked They have worked 8HMM8HMe! noKa3aTens:1M111 Heo6XOAlllMOCTlll yn0Tpe6ne- H111s:1 Present Perfect cny>KaT 06cTos:1TenbCTBa BpeMeH111: since (some moment), for (some time), ever, never, already, yet. I have lived here since my childhood. Mary has worked for three hours. Have you ever traveled abroacf? I have never traveled abroad. They have already called me. They haven't called me yet. HacTOR~ee coeepweHHoe npoAon>KeHHoe (Present Perfect Continuous) 06pa3yeTCS'I c noMOlJ.1blO BCnOMOraTenbHOro rnarona have B n1114HOH cj:JopMe HaCTOS'llJ.1ero BpeMeH111 + been + Participle I CMb1cnoeoro rnarona. 03Ha4aeT To >Ke, 4TO 111 Present Perfect Durative, HO nOA4epK111BaeT An111TenbHOCTb AelicTB111s:1: I have been living here since my childhood I have been working You have been working He, she, it has been working We have been working They have been working npoweAwee coeepweHHoe (Past Perfect) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona have B npoweAweM BpeMeH111 (had BO Bcex n1114ax 111 4111cnax) + Participle II CMblCno- eoro rnarona. 03HS4aeT AeHCTBllle B npownoM, npeAwecT- BOBaBwee APYrDMY AeHCTBllllO B npownoM: He had traveled abroad before he entered the uni- versity. I had talked You had talked He. she. it had talked We had talced They had tall<ed npoweAwee coeepweHHoe npoAon>KeHHOe (Past Perfect Continuous) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHoro rnarona have B npoweAWeM BpeMeH111 (had BO Bcex n1114ax 111 4111cnax) + been + Participle II CMb1cnoeoro rnarona 03Ha4aeT TO >Ke, 4TO Past Perfect, HO nOA4ep- KlllBaeT An111TenbHOCTb AelicTB111s:1: He had been traveling abroad before he entered the univer- sity. I had been talking You had been talking He, she, it had been talking We had been talking They had been talking 6yAy~ee coeepweHHoe (Future Perfect) 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTenbHOro rnarona will (Ans:1 nepBoro n1114a B03MO>KeH rnaron shall) + have + Participle II CMb1cno- eoro rnarona. 03H848eT AeHCTBllle B 6YAYlJ.1eM, KOTOpoe: a) 6yAeT 3aBepweHo K onpeAeneHHOMY MOMeHTy: He will have finished working by 5 o'clock b) npeAWeCTByeT APYfOMY AeHCTBllllO B 6YAYlJ.1eM: He will have finished working by the time I return. 6YAY~ coeepweHHOB npOAOn>KeHHoe 06pa3yeTcs:1 c noMOlJ.1blO BcnoMoraTe!lbHOro rnarona will (Ans:! nepBoro n1114a B03MO>KeH rnaron shall) + have + been + Participle II CMblcnoeoro rnarona. 03Ha4aeT TO >Ke, 4TO 111 Future Perfect, HO noA- 4epK111BaeT AnlllTenbHOCTb AeHCTB111s:1: He will have been working by 5 o'clock He will have been working by the time I return. 8HMM8HMe! Hiii OAHO 1113 6YAYlJ.1lllX BpeMeH He ynoTpe6ns:1- eTCS'I BnplllAaT04HblX npeAnO>KeHlllS'I BpeMeHlll Ill ycnOBllll'I, nplllCOeAlllHS'leMblX COI03aMlll Ill COI03- Hb1Mlll cnoBaM111 when, until, by the time, before, if, unless 11 /W I will speak to him when he comes. We shall go to the country if the weather is good. CTpaAaTe11bHb1lit 3a11or (Passive Voice) CTpaAaTenbHblH 3anor 06pa3ye'rcs:1 c noMo- lJ.1blO rnarona to be B HY>KHOH cj:JopMe + Participle II CMb1cnoeoro rnarona Active Voice Simple Present Mary helps John. Passive Voice John is helped by Mary. Present Progressive Mary is helping John is being helped by John. Mary Present Perfect Mary has helped John. Simple Past Mary helped John. Past Progressive Mary was helping John Present Perfect Mary nas heloea John has been helped by Mary. John was helped by Mary. John was being helped by Mary. .na.s been eloed o Mary. Past Perfect Mary had helped John. John had been helped by Mary. Simple Future Mary will help John. John will be helped by Mary. Future Perfect Mary will have helped John. John wilt have been helped by Mary. Ha1116011ee ynoTpe6111TenbHb1e Henpae111nbHb1e rnaronb1 arise arose arisen be was, were been become became become begin began begun bite bit bitten blow blew blown break broke broken bring brought brought buy bought bought catch caught caught come came come cost cost cost cut cut cut deal dealt dealt do did done draw drew drawn eat ate eaten fall felt fallen feed fed fed find found found fly flew flown forget forgot forgotten get got got give gave given go went gone have had had hear heard heard hide hid hidden hold held held keep kept kept know knew known lay laid laid lead led led lend tent lent let let let lie lay lain make made made meet met met pay paid paid read read read ring rang rung run run run see saw seen sell sold sold send sent sent shake shook shaken show showed shown/showed sing sang sung steep slept slept speak spoke spoken stand stood stood swim swam swum take took taken teach taught taught tear tore torn tell told told think thought thought understand understood understood wake woke/waked woken/waked l1Hc/JOpM8LjHOHHO-Cnpaeo~HaR ~ ra6nH4a "'C 000 •llHc/JOnnacr•. 2004 N 0 r. MocKBa, KlilllHpcKoe wocce. 21 V') '°E-mail matC1111opjastro _.. illfapjaslru '°0 r- 0
  • 16.
    HH4'0nAACT TM www.infoplast ru Cnoeapbnoec&AHeeHoro o6114eHMH O,qe>1<,qa Clothes BaM 3TO 1<1AeT! It looks good on you! KaKOH y sac paaMep? What's your size? 6enbe underwear 60COHOlKKl-1 sandals 6ornHK1<1 boots 6t0cnanbTep bra rancryK tie AeWeSblH cheap Alt<l-1HCbl jeans AOporoH expensive 30HT umbrella KOlKa leather KOnroTKl-1 pantyhose KOCTIOM suit KoweneK wallet KPYlKBSO lace KynanbHl-1K bathing suit KYPTKa jacket HOCKl-1 socks HOYHaR py6awKa nightgown nanbTO coat nepYaTKl-1 gloves n1-1lt<aMa pajamas nnaTbe dress nnaLJ.1-AOlKAeS1<1K raincoat nORC belt paaMep size py6awKa shirt pyKaS sleeve CS1<1Tep sweater cyMKa bag Tycpn1-1 shoes ¢YT60nKa T-shirt YynKl-1 stockings wanKa cap wapcj:J scarf wenK silk wepcTb wool wnRna hat wopTbl shorts t06Ka skirt ~eern Colours 6elt<eSblH beige 6enb1H white lKenTblH yellow aeneHblH green KOpi.1YH9SblH brown KpaCHblH red opaHlKeSblH orange p030SblH pink cseTnblH light cepblH grey Ci-1Hl-1H blue TeMHblH dark cj:J1-1oneTOSblH purple yepHblH black AeHbrH. 6aHK. noKynKH Money. Bank. To buy CKonbKO R saM AOnlKeH? CKonbKO 3TO CTOl-1T? 5'I 6b1 xoTen... no>Kany~cTa 3To AOporo! nOAasaTb >Kano6y 06Hani.141<1Tb YeK 3aKa3aTb onnaTi.1Tb CYeT 6anaHc 6aHKOSCKl-1H CYeT AaTa nnaTe>Ka AeHbrlol AOCTasKa aa se~ b noA 11Cbl0 How much do I owe you? How much is it? I would like... please It's expensive! to complain to cash a check to order to pay the bill balance bank account matunty date money de ery KOMaHAl-1POSKa KpeA1<1TKa Kypc (santOTbl) MenOYb H8ni.1YHble Hanor o6naraTb HanoroM o6MeHHblH nyHKT onnaTa OTABn npOAalK nepeSOA1<1Tb AeHbrn n1<1CbMeHHO noKynaTenb npOAaSaTb npOAaSel.I npOLeHT pacnpoAa>Ka business trip credit card rate small cash cash tax to tax exchange bureau payment sales department to transfer money in writing customer sell salesclerk interest sale pacXOAbl expenses peKnaMaL11<1R complaint c6epelt<eH1<1R savings CYeT (aa noKynKy, ycnyry) bill TaMO>KHR customs ToprosnR TpaTbl yH1-1sepMar ycnOBl-1R AOCTaBKl-1 ycnos1<1R onnaTbl LieHa l.eHHOCTb 3KOHOMl-1Tb (AeHbri-1) trade spendings department store terms of delivery terms of payment price value save money 3,qopoebe Health rAB y sac 6on1-1T? 5'I ce6R nnoxo YyscTsyt0. 5'I YYSCTBYIO ce6R npeKpacHo! Bbl sb1rnRA1<1Te 6onbHblM. 0TAOXHl-1Te! aHrn61-1ornK aHT1-1cenT1-1K aHrnHa anTeKa 6one3Hb 6onb B ropne 6onb 6pOHXl-1T spay rnnc rpaAYCHl-1K rp1-1nn A1<1arH03 ay6HaR 6onb 1<1HcpeKL1<1R Kann1-1 Kawenb KpOSb neKapCTSO Ma3b Mi.1KCTypa (OT KawnR) OlKOr onyxw1-1H naL11<1eHT nOHOC npocryAa pellem COnHeYHblH O>KOr cpeACTBO TeMnepaTypa (SblCOKaR) TOWHOTa TpaSRHO~ YaH yKon Where does it hurt? I feel sick I feel great! You look sick Rest! antibiotic antiseptic tonsillitis pharmacy illness; disease; sickness sorethroat pain bronchitis doctor cast thermometer flu diagnosis toothache infection drops cough blood medicine ointment cough syrup burn swollen patient indigestion cold recipe sunburn remedy fever nausea herbal tea injection; shot Yiie6a.Pa6oTa Studies. Workplace npOXOA1<1Tb Kypc (no...) (in...) 61-16n1<10TSKa 6i.13H9C-06yYBHl-19 6yxramep 6yxranrnpcK1<1H yYeT SBYepHee (OTAeneH1<1e, o6yYeH1<1e) ryMaH1<1TapHblB HayKl-1 AHesHoe (OTAeneH1<1e, 06yYeH1<1e) AOKn8A BCTeCTSeHHble HayKl-1 3aHRTl-1R 3ay1-1cneH1<1e to take a course library business studies accountant accounting part-time arts; humanities; liberal arts full-time report natural sciences studies enrolment 1<1306pa31<1TenbHOe 1<1CKYCCTBO fine arts 1<1HocTpaHHb1e R3b1K1<1 foreign languages 1<1Hcj:JopMarnKa computer sciences KaMnyc campus Kapbepa career KH1<1ra book KHl-1)f(Hb1H Mara31<1H Konnera KonneAlK Kypc MBCTO pa60Tbl 06paaosaH1-1e Ol.eHKa nonHaR 3aHRTOCTb npaso npenoAaSaTenb pa6orn pacn1-1caH1-1e peKnaMa cnosapb cneL11-1an1-1aaL11<1R cTeneHb 6aKanaspa CTeneHb cj:Ja6p1-1Ka YaCTl-14HaR 3aHRTOCTb WKOna 3K3aMeH 3HL11<1KnoneA1<1R t0P1<1A1<1YecK1<1H cj:JaKynbTeT bookstore colleague college course job education grade full-time work law professor work schedule advertising dictionary major bachelor (BA. , BSc) degree degree factory part-time work school exam encyclopedia law school E,qa. PecTOpaH Food. Restaurant 5'16bl XOTen... 5'I 6bl XOTen 3aKa3aTb... CYeT, nolt<anyHcTa! 06cny>K1-1saH1<1e sKnt0YeHo? 3a CTOnOM s1-1nKa ropY1<1L1a )KapeHaR KapTOWKa 3aSTpaK aaKyeKa Maeno HO)K nepel.I np1-1eM n1<1LJ.11<1 pacT1<1TenbHoe Maeno cancj:JeTKa COnb cneL.11-11<1 CTaKaH Cblp yKcyc yn1<1TKa xne6 I would like... I would like to order. .. The check, please! The service is included? At table fork mustard French fries breakfast appetizer butter knife pepper meal oil napkin salt spices glass cheese vinegar snail bread ftp cup chocolate egg
  • 17.
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  • 18.
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KaJKADe COCTaBHDe 'IMCflO MDlKHD pa3flDlKMTb Ha npDCTble MHOlKMTenM MnpM TOM TDflbKO eAMHCTBeHHblM cnoco6oM - 3TO OCHOBHIUI TEOPEMA APlr111>MEH1Klr1. np11Mep: 72=2·2·2·3·3=2'-3'. 'lro6b1 nony~11Tb :JTO paJ- no)l(eH11e, Ha110 pa311en11rb 72 cHa~ana Ha 2 (caMblii Ma- neHbKl1i111en11renb), nony~11M 36. 3areM y)l(e 36 pa311e- n11M Ha 2 (caMblii ManeHbKl1i111en11renb), nony~11M 18. npo11on)l(l1M, noKa He nony~l1M 3, KOTOpaf/ 11en11TCfl TOflb- KO Ha 3 11 nony~l1M I. 3ro 3an11- 72 2 AHanorn~Ho paJnO)l(l1M 180 2 Cb/8aeTCf/ 36 2 Ha npOCTble MHO)l(l1Ten11 90 2 TaK: 18 2 ~11cna 180 11 600: 45 5 9 3 9 3 3 3 180=2·2·5·3·3= 2'-5-3', 3 3 11 600=2·2·2·5·5·3=2'-5'-3 6onbW'1M noKa3aTeneM. Hanp11Mep, Ha11MeHbwee 06ll.ee KpaTHOe Y11cen 72, 180, 11 600 eCTb Yl1Cfl0 1800: HOK(72, 180, 600)=23 ·5'-3' = 1800. HOK- 3TO Y11cno, KOTOpOe Aenl1TC51 11 Ha 72, 11 Ha 180, 11 Ha 600. np11 3TOM Ha11MeHbwee 113 scex (3600 TO>Ke Aen11TcH Ha 72, 180 11 600, HO He HOK). Ha116onbw11ii 06ll.11ii Aen11renb (HOil) - npo113seAeH11e 06ll.11X npOCTblX MHO>Kl1Teneii, Ka>KAblii 113 KOTOpblX B351T c Ha11MeHbWl1M noKa3areneM. Hanp11Mep, Ha116onbw11ii 06ll.11ii Aen11Tenb Y'1Cen 72, 180, 11 600 eCTb Yl1Cfl0 12: HO,LI, (72, 180, 600) = 2'-3= 12. 06ll.11X Aen11Teneii (Y11- cen, Ha KOTOpble AenHTCH see 3Tl1 Yl1Cna) y 72, 180 11 600 HeCKOnbKO: 2, 3, 4, 6, 8, 12, HO 6onbwee 113 Hl1X - 12. B3aMMHO npoCTble '!Mena - ecn11 y Hl1X HeT 06ll.11X Aen11- Teneii, OTnl1YHblX OT I: HO,Ll,(3, 7)= I. Anil B3al1MHO npoCTblX Yl1Cen a 11 b cnpaBeAfll1BO: HOK(a, b) =a·b. .QeiicTBl1TenbHO, HOK (3, 7) =21. CB513b HOK(a, b) 11 HO,Ll,(a, b): HOK(a, b)-HO)J,(a, b)=a-b 4. npM3HaKM AenMMOCTM. 1) ecn11 Y11cno 0KaHY110aeTcR u11cppoii 0 11n11 u11cppoii 5, TO OHO AenMTCA Ha 5 (Ha I0 Aenl!TCR TOflbKO Yl1Cna, OKaHYl1BalOlJ.11eCR Ha 0). Hanp11Mep, Ha 511enRTCR: 10, 35, 125, 180, 2135; 2) ecn11 Yl1Cfl0 OKaHYl1BaeTC51 YeTHOii u11cppoii, TO OHO AenMTCR Ha 2. np11Mep: 4, 116, 358; 3) YT06bl Yl1Cno AenMnDCb Ha 3 He06XOAl1MO 11 AOCTa- TOYHO, YT06bl CYMMa era u11cpp Aen11nacb Ha 3. np11Mep: 9, 24 (2+4=6), 93(9+3=12), 132 (1+3+2=6); 4) '111Cfl0, COAep>Kall.ee He MeHee Tpex 1.111cpp, AeflMTCR Ha 4, ecn11 Ha 4 Aen11TCH '111Cno, o6pa3oBaHHoe noc- neAHl1Ml1 ABYMR u11cppaM11. np11Mep: 136 (36:4=9), 14356(56:4=14); Ha11MeHbwee 06ll.ee KpaTHOe (HOK) - npm130eAeH11e scex 5) nposepl1M Aenl1MOCTb Ha 7 ( 13) 6onbwora Yl1cna npoCTblX MHO>K'1Teneii, KaJKAblii '13 KOTOpblX B351T c Ha'1- 254390815. Pa3o6beM era no Tp11 u11cppb1 c KoHua: PaqMOHan1tH1tie 'IMCna 254 390 815. nonyYeHHble Tp11 Y11cna cno>K11M, Yepe- AYR 3HaK «+• 11 «-•, HaYaB c nocneAHera: +815-390+254=679. 3TO Yl1Cn0 Aefll1TCR Ha 7 (679:7=97), HO He Aefll1TC51 Ha 13. 3HaYl1T 11CXOAHOe Yl1Cfl0 254390815 KpaTHO 7, HO He Aenl1TCR Ha 13; 6) Yl1Cfl0, COAep>Kall.ee He MeHee YeTblpex Ul1¢p, AenMT- CA Ha 8, ecn11 Ha 8 Aen11TCH Y11cno, 06pa3osaHHOe noc- neAHl1Ml1 TpeMR u11cppaM11. np11Mep: 7360 (360:8=45), 598648 (64811en11TCf/ Ha 8); 7) ecn11 CYMMa u11cpp Yl1Cna AenMTCA Ha 9, TO 11 caMO Yl1Cfl0 Aefll1TCR Ha 9. np11Mep: 2952 (2 +9+ 5+2= 1811enl1TCf/ Ha 9); 8) YT06bl ABYX3HaYHOe Yl1Cfl0 6blCTpO YMHO>Kl1Tb Ha 11 , H3AO pa3ABl1HYTb era u11cppbl, a Me>KAY Hl1Ml1 nocra- Bl1Tb 11X CYMMy. np11Mep: 53· I I= 5(5+ 3=8)3=583, 36· I I=396, 47·11=4(4+7= l 1)7=4(11)7=(4+ 1)17=517; rpeX3HaYHOe Yl1Cfl0 Aefll1TC51 Ha 11 , ecn11 BTOpaH era u11cppa eCTb CYMMa ABYX APYrl1X. np11Mep: 143(4= I +3), 572(7=5+2); YT06bl MHOra3HaYHOe Yl1Cno Aen11nocb Ha 11 , H3AO YT06bl CYMMa era u11cpp, B3RTblX c «+ ». ecn11 u11cppa Ha HeYeTHOM Mecre (HaYl1Ha51 OT eAl1- H11U). 11 c «- », ecn11 u11cppa Ha YeTHOM MeCTe, Aen11- nacb Ha 11. np11Mep: 24569He11enl1TCfl Ha 11 , T.K. +9 - 6+5-4+2=6- He 11en11TCfl Ha 11 , 2694615 (+5-1 +6-4+9-6+2= I l)-11en11TCR Hal I; 9) Yl1Cfl0, COAep>Kall.ee He MeHee Tpex 1.111cpp, Aenl1TCR Ha 25, ecn11 Ha 25 Aenl1TCR Yl1Cfl0, o6pa30BaHHOe nocneAHl1Ml1 ABYMR u11cppaM11. np11Mep: 125, 7675, 1850; 10) Yl1Cfl0, COAep>Kall.ee He MeHee YeTblpex U11¢p, Ae- fll1TCH Ha 125, ecn11 Ha J25 Aefll1TCR Yl1Cfl0, o6pa- 30BaHHOe nocneAHl1Ml1 TpeMH u11cppaM11. np11Mep: 5125, 7375, 1750. llppaQM0Han11H1111 'IMCna Pau110HaJJbHb1e Y11cna-Y11cna B11Aa !ff. rAe m- uenoe (mEZ), n - HaTypaJJbHOe (nE N). MHO>KeCTBO pa1.1110HaJlbHblX Yl1Cen o6o- 3HaYalOT Q(N - YaCTb z. a zBXOAl1T B Q). n106y10 6eCKOHeYHYIO AeCRTl1YHYIO nepl10Al1YeCKYIO AP06b MO>KHO npeACTaBl1Tb B Bl1Ae o6blKHOBeHHoii AP0611: 0,3 ( 18)=J.2. JS 11 ef6 - 11ppau110HaJlbHble Yl1C- na, Bblpa>KalOTCR 6eCKOHe~HOi111e­ Cf/T11~HOi1Henep1101111~eCKOi111po- 6bl0. CaMoe 113secTHoe 11ppa1.1110- HaJlbHoe '111Cfl0 - .n:=3, 141592... 3anl1Cb paq110HanbHOrO ~11cna 8 81111e 6ecKOHe~HOi1 11ecf/T11~Hoi1 nep1101111~ecKoi1 11po611: 5=5,00000... =5,(0) 8,377=8,377(0) 7 22 =0.31818... 18...=0,3 (18) - 6ecKOHeYHa.ll nep110A11YeCKa51 AP06b c nepMOAOM 18 (pa3Aen11n11 7 Ha 22 •yronKOM•). nl060e paU110HaJlhHOe Yl1Cfl0 0 aeCRTH't 01 JI.POOH MIHI B B _e 6ec o~e 0. ne np11Mep: Jan11caTb 8 81111e 06blKHOBeHHOi111P0611 1,(23) 11 1,5(23). I cnoco6: 1) nono>K11M x= 1,23232323... 2) nepeABl1HeM 3anRTYIO Ha DAMH nepM01r IOOx = 123,2323... 3) 113 JOOx BblYTeM x: IOOx-x= 123,23... - 1,23..., 99 -12J _ 122T.e. x- -· 3Ha'll1T x-99 4) l (1')_ 12:! -1 :!311TaK. • -~ - 99 - 99 II cnoco6: 1,.: _ = 1..: - 0. _.)= li --:=1:-=-- - OTHOWeH11e Afll1Hbl n1a6oii OKPY>K- HOCTl1 K ee Al1aMeTpy (.n:- OT rpe'le- CKOro nepwf!ep11R - OKPY>KHOCTb). Llt=- D
  • 19.
    Cpe,qHee ap11cjJMern~ecKoe Y11ce11a 11 b- Y11c110 a; b, cpe,qHee reoMerp11~ecKoe - .,Joi . CpeAHee ap11cj)MernYecKoe ABYX Heorp114are11bHblX Y11ce11 60JlbWe 111111 paBHO 11X cpeAHeMy reoMeTpl1'18CKOMy: a;b'?:--Joi. reoMerp11~ecK11ii CMb1cn. Bnp11Moyro11bHOM rpeyro11bH11- 1. 06blKHoaeHHb1e AP06M Apo6Hb1ii 3HaK 3aMeH11er 3HaK Ae11eH1111. i= 1: 6 ' I - B'll1Clll1Te11e, 6 - B3HaMeHaTelle. npaBl1flbHaR ,4p06b - y KOTOpOii '111C1111Tellb MeHbWe 3Ha- MeHaTell!I. HenpaBl1nbHaR ,qpo6b - y KOTOpoii '111C1111Tellb 6011bwe 3HaMeHare1111 111111 paseH eMy. OCHOBHOe CBOiiCTBO ,qpo611: ec1111 '111CJ111Tellb 11 3HaMeHa- Tellb YMHOJKl1Tb 111111 pa3Ae1111Tb Ha OAHO 11 TO JKe '111CJ10, TO no11yY11rc11 pasHaR eii AP06b. 1 1·3 3 3 3:3 I 6= 6-3=18 ' 18 = 18 :3 =6 npMBeCTK AP06K KHaKMeHbWeMy 06lJ.leMy 3HaMeHaremo: 1) Hai1r11 HOK (Ha11MeHbwee o6ll.lee KpaTHoe) 3HaMeHare- 11eii AP06eii, 2) Haiir11 AOnOJlHl1TellbHble MHOJK11Te1111 (pa3- Ae1111Tb HOK Ha KaJKAblii 3HaMeHare11b), 3) YMHOJKl1Tb Y11c- 1111renb 11 3HaMeHaTellb Ha COOTBeTCTBYIOlJ.ll1ii AOnOl1Hl1- TellbHbli1 MHOJKl1Tellb. Hanp11Mep, np11seAeM AP0611 t,t 11 tKo6ll.leMy 3Ha- MeHare1110. ):1111 aTOro HaiiAeM HOK(3, 5, 7) = 3·5·7 =105. Aono11H11re11bHb1e MHOJK11- re1111 y t-3TO 5 11 7' y t-3TO 3 11 7' y t-3TO 3 11 5. 3an11weM 11Xcsepxy, OTA81111B CK06Koii. YMHOJKl1M 11 '111C- 1111T8Jlb 11 3HaMeHaTellb Ha 3Tl1 AOnOl1Hl1T8JlbHble MHOJKl1- Te1111: 1°' 1· 5·7 35 -3-= 3.5.7 = 105 · .r.:::_ = 2·3·7 = 42 5 5.3.7 105 ' 3' 35 3.3 .5 45 -7- = 7.3. 5 105 . CpaBHMTb AP06M: 1) np11secr11 11x K06lJ.leMy 3HaMeHare1110, 2) cpaBHl1Tb Y11c1111re1111 no11y'!eHHblX APD6ei1, 3) cpaBHl1Tb no11y'!eH- Hble AP0611, 11 re JKe 3HaK11y11cXOAHb1X AP06ei1. CpasH11M AP0611 !,t11 t.K o6ll.leMy 3HaMeHare1110 I 35 2 42 3 45 npl1senl1: 3=105 · 5 =105 11 1= 105 · nponop41111 - 3TO paseHCTBO ABYXOTHOWeH11ii. np11Mep· 2 • 5 =12 111111 2 5·5=3 5·7. 5 7 ' . , . Hepa18HCTIO KIWI Ke 113 np11Moro yrna nposeAeHbl KrnnoreHy3e BblCOTa h 11 MeA11aHa. nycTb Bb1cora Ae1111r rnnoreHy3y Ha orpe3Kl1 a 11 b, TOrAa h =.,Joi (113 re0Merp1111). no11os11Ha rnnore- HY3bl - 3TO a;b , a 113 re0Merp1111 3HaeM, '!TO MeA11aHa, nposeAeHHaR KrnnoreHy3e, pasHa no11os11He rnnoreHy- 3bl: m=a;b . TaK11M o6pa30M, HepaseHcTBo Kow11 03Ha- Yaer, '!TO AJ111Ha BblCOTbl, npOB8A8HHOi1 KrnnoreHy3e, ,Apo61 CpasH11M Y11c1111re1111 no11yYeHHblX AP06eii: 35 <42 <45, 3Ha'll1T 11 AP0611 pacno11ara10rc11 a TOM JKe nopRAKe: 35 42 45 105 < I 05 < 105 ' C118AOBaTellbHO, MOJKHO cpaBHl1Tb 11C- XOAHble AP06W t< ~ < t. CnoJKeHKe KBbl'IKTaHMe AP06eii. 1) c OA11HaKOBblM 3HaMeHare11eM (nOABOA11M nOA 06lJ.ll1i1 3HaMeHaT8Jlb 11 CKllaAblBaeM 'll1Clll1Te1111) .!.+ ~= 1+ 2 =l 5 5 5 5 2) c pa3HblMl1 3HaMeHare1111M11 (np11secr11 AP0611 K06lJ.le- MY 3HaMeHare1110, n0Asecr11 noA OAl1H 3HaMeHaTellb, npo- secr11 sb1Y11c11eH1111 c Y11c1111re1111M11): l[' 1<3 5 3 5+3 8 3 + 5=15 + 15 = 15 = 15-. l(J 5<• 3 5 8 4 6 + 18 = !8 +!8 = !8 = 9· YMHOlKeHKe KAeneHKe AP06eii. 'iT06bl nepeMHOJKl1Tb ABe AP0611, HaAO nepeMHOJKl1Tb OT- AellbHO 11x Y11c1111re1111 (3TO 6yAeT Y11c1111re11b) 11 11x 3HaMe- Hare1111 (3TO - 3HaMeHare11b no11yYeHHoii AP0611): 2 4 2-4 8 3·5 = 3-5= 15. 'iT06bl pa3Ae1111Tb OAHY AP06b Ha APYrYID, HaAO nepsylO AP06b YMHO)f(l1Tb Ha «nepeaepHyTy/O» BTOpylD: ~ :~ = ~.i = ~:!= ;~ . 'iT06bl npeACTaBl1Tb 06blKHOBeHHYIO ,qpo6b B811,qe ,qecR- Tl1~HOii, HaAO pa3Ae1111Tb '111CJ111Tellb Ha 3HaMeHaTellb «BCTOJ1611K». np11Mep: l/ 4=0,25, 1/ 3=0,(3) - 6eCKO- He'!Ha!I nep110Al1'!eCKa11 AP06b. 2. .QecRTM'tHble AP06M OKpyrneHMe AO AaHHOro pa3p!!Aa: ec1111 ClleAYIOlJ.la!I l.111QJ- pa 0, I, 2, 3 111111 4, TO 11x npocTO 3aMeHRIOT Hy1111M11, a ec1111 c11eAY10lJ.l11e 411cjlpb1 5, 6, 7, 8, 9, TO noc11eAH1010 OCTaBWYIOCA 411cjlpy yseJ111'111BalOT Ha I, a OCTallbHble 3a- MeH!llOT HYl1AMl1. np11Mep: OKpyr1111M AO COTblX15,3467. 3AeCb 'leTblpe CO- TblX, 3a Hei1-6, 3Ha'!l1T, YersepKy 3aMeH11M Ha 5 (4+ 1), a OCTallbHble 3aMeHl1M HYl1AMl1: 15,3467= 15,3500= 15,35. Dponopq11 MeHbWe 111111 pasHa AJ111He M8A11aHbl, npoBeAeHHOii Krn- noreHy3e: hsm. a b OKpyrn11M AO TblCA'!HblX2,384256. TpeTbR noc11e 3anA- TOii - 4, 3a Heii 2. C11eAosare11bHO, 4 He MeHReM, a see, '!TO 3a Hei1 3aMeHAeM Hy11AM11: 2,384356-2,384000=2,384. CnolKeHKe (Bbl'll1TaH11e) BblnOllHAIOT no pa3PRAaM: AP0611 3an11cb1Ba10TAPYr noA APYrDMTaK, '!T06b1 3anATaA crporo nOA 3anATOii HaXOA1111aCb, 11 BblnOJlHAIOT CJlOJKeH11e (Bbl- 'll1TaH11e) Ha'!11HaA c caMoro npasoro pa3pRAa. CllOJKl1M 3,4682 11 48,63: + 3,4682 48,63 52,0982 v13 67,2 Bbl'!TeM 5,375: _ 67,200 5,375 61 ,825 YMHOJKeHMe BblnOJlHAeTC!I He o6palJ.laA BHl1MaHl1e Ha 3a- nRTble, Bno11yYeHHOM pe3y11bTaTe cnpasa OTC'll1TblBalOT CTOllbKO 3HaKOB AD 3an11TOii, CKOJlbKO 11XCTOl1T noc11e 3a- nRTOii B06011x MHOJKl1Tell!IXBMecre. np11Mep: 3,02 · 1,4 - noc11e 3anATblXscero rp11 3HaKa, 3Ha'!l1T, a no11yYeHHOM pe3y11brare OTAe11AeM 3an11TOii rp11 3HaKa cnpasa: 3,02 x 1,4 1208 + 302 4,228 ,Qe11eHMe. B06e11x AP06Ax nepeHecr11 3amny10 Ha CTOllb- KOl.111QJP snpaso, CKOllbKO 11XBAe1111re11e (TO, Ha '!TO Ae- 1111M) 12,096:2,24 = 1209,6:224; a 3areM Ae1111M Ha 4e- 11oe '111Cl10 B«CTOl1611K»: _1209,61224 illQ__ 5,4 896 896 0 YMHOJKeHMe Ha IO" - nepeHecrn 3an11ry10 Ha n 411cjlp snpaso. np11Mep: 5,238 ·100 = 5,228 ·IO' = 523.8 Pa3AenKTb Ha I0 a creneH11 n - nepeHecr11 3anATYID Ha n 411cjlp s11eso. np11Mep: 2,7: 1000= 2,1:10' =0,0021 A npRMO nponopl.(110HanbHa B c Ko3cjJcjJ111.(11eHTOM nponopl.(l10HanbHO- cr11 k = j .Yse1111'!11s A arp11 pa3a, B yse1111'!11TcR TOJKe arp11 pa3a: 3AeCb 2,5 11 7 - KpaiiH11e '!lleHbl nponop41111, a 5 11 3,5 - cpe,qH11e YlleHbl nponop41111. np0113B8A8Hl1e KpaiiHl1X'!JleHOB = np0113B8A8Hl1IO BHYTP8HHl1X '1118HOB: 2,5·7= 5·3,5 3-A =k·3B, a K03QJQJ11l.111eHT k np11 3TOM He MeHAeTCA k = ~~ . Ase ee1111'!l1Hbl Ha3b1sa10rc11 o6paTHD nponop11MoHanbHblMM, ec1111 np11 yse- 1111'feH1111 OAHOii 113 Hl1XBHeCKOllbKOpa3, BTOpa.R YM8HbWaercR BO CTOJlbKO JKe pa3. A o6paTHO nponopl.(110HanbHa B c K03c/JcjJ111.(11eHTOM nponopl.(110- HanbHDCTH k: A= k i. 'iT06bl HaiiTM HeK3BeCTHblii 'IJleH nponOPllMM, HaAO npOl13B8A8H11e 113BeCT- HblX'!JleHOB pa3Ae1111Tb Ha napHblii '1118H KH8113BeCTHOMy: 0, 3 - 2, 5 .. 2 - = 0 3. - = 0,3. 5 = Q = 0 6 x - 5 ' _, .) . ). x 2.5 2.5 . Ase se1111'!11Hbl Ha3b1sa10rc11 np11Mo nponop11MoHanbHb1 'leHl111 0,11HOM 113 l1X 8 ec Ollb 0 pa3 BTOpa.R yae- HBaeTCll BO .e Pa3 ..f=kB. se,1 ~ B 4 B PM p<Ua, B e b HTCA TO e 8 TPH p33a· 3A = k -% ' 1k=.f B Bell ~ "' ""N "'.., ~ .., 0 ,.._ 0 ..,
  • 20.
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HacneACTBeHHOCTb - c0oilicrno coxpaHHTb Ill nep8A888Tb np1113H8Klll CTpOeHlllfl, c:jJyHK41111 OT POAlllTeneH K n oTOMCT- ay. HacnBAYIOTCfl np113HaK11, 3an111caHHb1e a reHoT11ne. D lfapnb3 ,qapBHH - Hacn8,qcrneHHaJ1 113- MeHY110ocTb, 6opb6a 38 cylljBCTBOB8Hl1e VI 8C- TBCT8BHHbllii oT6op - As11)1(yl.J..V1e c111nb1 30ont0- Lllll1 opraHl1Y8CKOro Ml1pa Vl3MeH41180CTb - c0oilicrno 1113M8Hf1Tb 1-1 np1106peTSTb H08bl8 I1p113H8Kl1 8 npBABnax 81<1AB· EcTeCTBBHHblM OT6op - rnaBHblili c:jJaKTOp, onpeA8IlfllOl..L11ili Hanpa8Jl8HHOCTb 3BOill0411lll. P onb OT61-1pa10IJ..8ro c:jJaK- TOpa 111rpa10T ycnOB1fl OKpy>KalOIJ..Bili CPBAbl B pe3yilbTaTe ABJA>Kyll.jero ecrecrneHHoro OT6opa npelllMYl..LBCTBBHHO coxpaHflK)TCR oco611c1113MeHeH111flMl1, a crn6JA- nJA3JAPYIOUJero - co CTa6111JlbHblMl1 np1113H8KSMl1, COOT8eTCT8YIOIJ..11Mlll cpeAB 0611TBHl1fl . ...________........__.. p----------------41-1TOflOrlll5'1 - HayKa 0 CTp08Hl111 VI c:jJyHK41110H11pOBBHl111 KJ18TKl1. OpraHl13Mbl : 0cHOBHbl8 nonm1<8Hl15l KJ18T04HOH Teop111-1 6b1Jll1 cc:jJopMy.n111posaHbl M. WneHABHOM Ill T. W8aH- 0 npoKap1-1oni14ecK1-1e (6aKTep11111, ClllHe-38Jl8Hb18) - KJ18TKl1 He HOM: see opraHU3Mbl (paCTl1T8nbHb/8 11 )KJABOTHb!B) COCTORT JA3 Kfl8TOK. 1<1MBIOT o¢opMI18HHOro HAPS l<1 MHOrl1X opraHOlllA08; CoepeMeHttaR KneT01..1Has:i Teopiui: o 3yKap1110T1111..1ecK111e {rp116b1, pacTeH11.fl, )l(lll80THb1e, 48Il08eK). 1. K nBTKB ~ BA11H1114a cTpoeH1111 111 pa3e111T1111 0cex opraH1113MOB. 2. KneTKl1 opraHl13M08 pa3HblX 4apCT8 )1(1180lii np11pOAbl CXOAHbl no CTpOBHllllO, Xl1Ml148CKOMY Cyl.J..BCT8Y8T H8KJ18TOYH851 c:jJopMa )l(l-13Hl1 - e111pycb1, KOTOpb18 COCTa8y, o6MeHy 8 8 1.J..8CT8, OCH08HblM npOfl8Jl8H1flM )1(1113H8A8flT8JlbHOCTl1. cnoco6Hb! >Kl1Tb 11 pa3MH0)1(8TbC5l TOJlbKO 8 KJ18TK8X APYrl1X opraHl/13- 3. Ho8bl8 KJ18TKlll o6p83YIOTCfl 8 pe3y.nbTBTe A8I18Hl15l MBT8plllHCKOiii KJ18TKl1. 4. B MHOroKnBT04HOM opraH1113MB KJ18TK11 o6pa3yK)T TKBHlll. 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L111Tonna3MB npOHl138HB 6enK08blMVI Ml1KPOTpy6o4KSMl1 , o6pa3YIOIJ..VIMl1 411TOCK8Jl8T KJ18T- Kl1, 6naroABPfl KOTOpOMY KflBTKa coxpaHRBT noCTOflHHYIO c:jJopMy. flJA30COMbl - «Jll1ll_8BBp11T8JlbHb18 CT3H411111» KJ18TKVI, pBCUBnilfllOT CJ10)1(Hbl8 opraHl1Y8CKl18 88U8CT89 HS 6onee npoCTblB MOJlBKYilbl. Ml-ITOXOHP,p!A11 - «Cl1110Bbl8 CTBH41-111» KflBTKl-1, Cl1HTe3 AT<D, 11CT04HlllK 3H8pr1111. B nnacmp,ax {KneTKlll pacTeH11ili) OCYIJ..BCTBnReTcs:i c11HTB3 opraH11LJBCK111x 0ellecrn. neiliKonna- CTbt - 6ec4eeTHble nnaCT11Abl, HaKannl1BBK)T KpaxMan. XpoMonnaCTbl - C1HT83 K6p0Tl1H011A0B (>K8Jl- Ta5l, opaH)l(88Bfl, KpacHafl OKpacKa nnOAOB, 4eeTKOB). XnoponnaCTbl - 38Jl8Hbl8 nnaCT11Ab1, COABP- )1(3T xnopo¢mnn. XpoMo- VI xnoponnacTbl yyacTBY'°T e c:jJornc11HTB3e. BaKyon11 HaKann11sa10T nVITBTBJlbHblB Bel..LBCTBa 11 npOAYKTbl pacnaAa 8 8BKyOnbHOM COKB. no- CTOflHHb18 BBKYOI111 - B paCTl1TeflbHOlii KJleTK8, AO 90% 06b8MB. Bp8M8HHbl8 BBKYOI111 - 8 >Klll80THOi1 KJ18TK8, HB 6onee 5% 06beMa KJ18TKl1 3nc (3HAOnna3M8TW-leCKBfl C8Tb) - rnHT83 Jllllfl11A08 Ill yrne80A08. 3nC - r.naAK8fl 11 wepoxo0a- T8l'l (BCTb p1160COMbl, OHi/i Y4BCTBYIOT B Cl1HTe3e 6enK08). KneTOYHblif Lj8HTP {2 48HTp111on11) YYBCT8YBT B ABI18H11lll KI18TOK, 06pa3yeT sepeTeHO ABI18Hl1s:l. KoMnneKC ronb,D,JKJA - TpaHcnopTHO-HaKon11TenbHa.fl c:jJyHK41-1s:i, c:jJopM111posaH11e n113ocoM, Kne- TOLJHoili o60Jl0YKlll nna3M3Tl148CK35l MBM6paHa n111H0411T03HblB ny3b1pbKl1 MlllTOXOHAP11H 3H,qOnnB3MBTl1LJBCKBR CBTb KoMnneKcronbP,>Kl1 ""~~1.-XPOM8Tl1H l---/-;iJP-'-'-1- flAPblWKO 5'1ABPH85l MeM6paHa L111Tonna3Ma ~L!::::=::;;;.,,__ BaKyOnb R!Jpo KneTKl1 (6onbWVIHCTBO KflBTOK opraH113MOB 111MeeT CAHO HApo. HO BCTb Ill 683- , A8Y-, MHOr051ABPHbl8 KJleTKVI}" Rp,epHaR o6onoYKa 06ecne4110aeT nocTynneH111e 6enK00, >K111po0, PHK, yrn8BOA08, BOAbl , 1-ioHOB. R.qepHblM COK - KOH4eHTpa41151 8C8X 8811BCTB. 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  • 21.
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  • 22.
    HH4'0nAACT: TM l>ICWAH MkTEMAl+--~---r---' 1) IlOCTOJIHHl>rii MHOl!GITeJJb MO)f(HO BhIHOCHTb 3a 3HaK HHTerpana: Jaf(x)dx =aJf(x)dx 2) l1Irrerpan cyMMbl (pa3HOCTH) paBeH cyMMe (pa3HOCTH COOTBeTCTBeHHo) HHTerpaJIOB: I (f + g-h)dx =I fdx+ I gdx- I hdx 3) l1IrrerpnpoBaHHe no 'laCTHM: Judv = uv - Jvdu 4) IlpaBHJIO no,z:i;CTaHOBKH: ecJIH x = <p(t), TO I 1cx)dx= I f[<p(t)]·<p'(t)dt OcHoeHb1e T11mb1 1o1HTerpanoe c np1o1MepaM1o1 peweHMH 1) U:emur paUHOHaJlbHaH cp~: IlpHMep: J(x5 +4x3 -2x2 -3x+2)dx = = Jx5dx+f4x3dx-J2x2dx-J3xdx+f 2dx= x6 x4 x3 x2 = -+ 4 ·- - 2 ·- -3 ·- + 2x + c = 6 4 3 2 x6 4 · 2 3 3 2 =-+x --x --x +2x+c 6 3 2 2) l-OJo6HlUI pal{HOHaJJbHllil cp~: IlpHMep: I 2x +1 dx =J 2x+1 dx x2 -4x+3 (x-l)(x-3) Pa3JIOlKllM nO,LhIHTerpaJlbll)'IO cpyHKl{HJO Ha npocrhle ,z:i;po6H: 2x+l A B - - - - - = --+-- (x-l)(x-3) x-1 x-3 IlpHBO,LHM K 0611:1eMY 3HaMeHaTemo: 2x+l A(x-3)+B(x-1) (x-l)(x-3) (x-l)(x-3) 2x+l = A(x-3)+ B(x-1) 2x+l = (A+B)x-3A-B IlpnpaBHHBaeM K03cpcpHl{HeHTbl npH O,LIHHaKOBhIX creneHJIX x: { 2=A+B {A=-% PemaeM CHCTeMY: 1= -3A-B B = 7_ 2 3Ha'IHT, I 2x+ 1 dx- _iJ dx +7-J__!!!_- (x-l)(x-3) 2 x-1 2 x-3 =-i Jd(x-1) +2 Jd(x-3) = _11nJx-1J+7__1nJx-3J+c 2 x-1 2 x-3 2 2 3) l1IrrerpnpOBaHHe BhlpIDKeHJtii: BH,La Xm (a +bx")p dx : l1IrrerpaJI TaKOro BH,La MOlKeT 6hITh BhipIDKeH B JJieMeHTapHbIX <P~ TOJihKO B lpex crry•raJDc • ecJIH p - u:erroe 'IHCJIO, TO (a +bx" ) B03BO,LHM B CTeneHh p, pacKp1>maeM CK06KH H HHTerpnpyeM KalK,Loe cmrraeMoe; m+l • ecJIH p - He u:eJioe, HO - - - u:eJioe 'IHCJIO, To npHMeIDierc.11 n no,r:i;CTaHOBKa BH,La t = )a +bx" , r,z:i;e r - 3HaMeHaTeJih ,z:i;po6H p; n+l I x"dx =~+ c,(n :t-1) n+l Jdx =lnJ~+c x Iexdx=ex +c ax I axdx=-+c Ina Jsin xdx =-cosx+c Jcosxdx =sin x+ c Jtgxdx = - lnJcos~ + c Jctgxdx =lnlsin ~ + c J4=tgx+c cos x I dx -.-- = -ctgx +c Slll 2 X I shxdx =chx +c m+l Jchxdx =shx +c I thxdx =lnJchxj + c Jcthxdx =Inlshxj + c I ~ =thx+c ch x I_!!!_= -cthx +c sh2x I dx 1 x --- =- arctg-+ c a2 +x2 a a J~=-1 1n[a+x[+c (01mJ~<a)a -x 2a a-x J~=-1 ln1x-a[+c (OJl}lJ~>a)x -a 2a x+a • ecJIH - - + p - u:erroe 'IHCJIO, TO HCITOJih3yeM ITO,LCTaHOBKY n 4) TpttroHOMelpH'lecKHe cpYffKllHH: JR(sin x) ·cosxdx pemaeTC.11 rro,11craHOBKoil t =sin x; cosxdx = dt; JR(cos x) ·sin xdx pemaeTC.11 rro,11craHosKoil t = cos x ;sin xdx = -dt ; I sin n x. cosm xdx CBO,LHTC.11 K nepBOM)' CJIY'IalO HJIH KO BTOpOM)', eCJIH XOT.11 6bl O,LIHO H3 n H m - He'leTHO: IJpHMep: Jsin 2 x·cos5 xdx=Jsin 2 x·cos4 x·cosxdx= = Jsin 2 x·(l-sin 2 x)2 ·cosxdx= Jt2 (1-t2 ) 2 dt, r,z:i;e t=sinx EcJIH lKe o6a n H m 'leTHbie, TO crerreHH MOryT 6hITh CHHlKeHbI B,LBOe C IIOMOill:blO cpOpMYJI: . sin 2x . 2 1- cos 2x 2 1+cos2x Slll XCOSX = - - · Slll X = · COS X = ----2 , 2 , 2 IlpHMep: Jsin 2 x·cos4xdx =J(sin xcosx)2 cos2 xdx = = ~Jsin 2 2x ·(1+cos2x)dx = = .!.Jsin2 2xcos 2xdx+ _!_ fCl-cos4x)dx = 8 16 = _!_Jsin2 2xd(sin 2x) + _!_Jldx- - 1-Jcos4xd(4x) = 16 16 16·4 1 sin 3 2x 1 1 . = - ·- - - +- X - - •Slll 4x +C 16 3 16 64
  • 23.
    EcJIH ff (x)dx=F +c , TO crrpaBe,!UIHBa <l><>PMYrra HLIOTOHa-Jleii6mnm: b ff(x)dx = F(b)- F(a) 0cHOBHble CBOHCTBa: b a 1) ff(x)dx=-f f(x)dx b b c b 2) ff(x)dx= ff(x)dx+ ff(x)dx a c b 3) fU(x)+ g(x)-h(x)]dx= a b b b = ff(x)dx+ fg(x)dx- fh(x)dx a b b 4) fcf(x)dx =cf f (x)dx a a 5) ff (x)dx = 0 6) reoMcrpH'!ecK.Hii CMMcrr orrpe,11erreHHoro mrrerparra: ~(x) yb ff(x)dx=S s a b x 7) TeopeMa o6 ou:eHKe H11Terparra: b m(b-a) ~ ff(x)dx ~ M(b-a) a f,11e m - HaHMeHDIIIee 3Ha'feHHe f(x) Ha [a,b]; M - HaH6oJibIIIee 3Ha'feHHe f(x) Ha [a,b]. b 1) ff (x)dx = F(x)I: 2) IIpaBHJIO IIO,!ICTaHOBKH: X =<p(t) b ;-1(b) ff(x)dx= ff[<p(t)] ·<p'(t)dt ;-i(a) 3) mrrerpHpOBaHHe no 'faCTJ1M: b b b ff(x)dx = fudv = uvl:-fvdu a a fipHMep: I I I fxexdx =fxdex =xexl~ - fexdx = 0 0 0 =e-(e - 1) =1 4) rrpH6JIIDKeHHoe Bbl'fHCJieHHe HllTerparros: fipHMep: Yz Bbl'fHCJIHTb I= fe-x'dx c TO'fHOCTblO ,!10 0,0001 0 x2 x4 x6 xs e-x' = 1- 1!+ 2! -3!+ 4!- ... , 3Ha'fBT, , x2 x4 x6 x fe-x dx= x(l -1!·3 + 2~5 - 3~7 + 4~9 - ...). OTK}',!13 Yz 2 1 1 1 I= fe-x dx=l(l- 22 ·3·1!+ 24 ·5·2!- o 1 1 - + - ...)"" 0,4613 26 . 7 .3! 28 . 9 .4! Pa3nO>KeH"1e OCHOBHblX <l>YHK4"1M B P~Abl m(m-1) 2 (l ± xr = l±mx+ 2, x + ...+ nm(m-1)...(m -n+l) "+ lj<l· +(-1) x ..., ..1 ' n! 3 5 2n+l . x x l)" x + .sm x=x--+-- ...+(- -···· 3! 5! (2n +1)! 2 4 x2n COSX = 1- .::.._+.::__-...+ (-1)"--±...; 2! 4! (2n)! 2 xn x 1 x . x + + .e = +- + -+... - ..., 1! 2! n! x2 x3 ln(l+x) = x-2 +3-...+ + (-lr+'xn ± ..., (-l<x~l). n 5) rrpH6JIIDKemn.1e MeTO,!lbI: ipopM)'rra IIpllMOyrOJlbHHKOB b b-a ff(x)dx"" -n-(Yo + Y1 + ...+ Yn-1) a ipopM)'rra T}JaIIeiulli b b-a f f(x)dx ""--(y0 +2y1+2y2+ ...+ 2n ) a +2Yn-I+Yn <l><>PMYJI3 rrapa6orr (CHMIICOHa) - .!IJIJl 'feTHOro n: b b-a f f(x)dx,,,,--(Yo +4y1 + 2y2 +4y3 + 3n a +...+2Yn-2+4Yn-I+ Yn) ( +br+' f (ax +b)"dx ax + c,(n :t:-1) a(n+ 1) f ax+b dx=~x+ bf-,ag Inlfx+ gl+c fx + g f 1- dx f(ax+b)(fx+ g) fax2 +~x+c = 2 l 1nlfx + g l+c, bf - ag ax +b (bf - ag :t: 0) =-===arctg - --- c. ...., 4ac - b- fax2 :;,x+c = 1 2ax+b-"1b2-4ac - ===ln +c, -..)b2- 4ac 2ax+b +-..Jb2- 4ac (b2 - 4ac >0) f~(ax+:fx+g) = _2_Inl~a(fx+ g) +~f(ax+b)l +c, -{<if af >O 2 ~arctg -v - af f(ax+b) +c, af <0 a(fx+ g) f~fx+ g dx = _!_~(ax+b)(fx+ g)- ax+b a bf-ag f dx +c 2a ~(ax+ b)(fx +g) ' f"1a2-x2dx= = _!_ (x"1a2- x2+ a2arcsin ~) + c 2 a f"1x2 +a2dx = = ~(x"1x2 +a2+a2lnlx+"1x2+a2i) + c f"1x2-a2dx= = ~(x"1x2 -a2- a2 Inlx+"1x2-a2 i) + c f sin ax xcosax xsinaxdx=- -2 - - +c a a f cos ax xsin ax xcosaxdx=--2 -+ +c a a fInxdx=xlnx-x+c f . x . x rz-2) arcsm - dx = xarcsm-+ '/a- - x- + c a a f x x rz-2)arccos-dx = xarccos--'Ja- - x- +c a a f x x a I 2 2I)arctg-dx = xarctg---In a +x +c a a 2 farcctg ~dx = x a .1 , 21)= xarcctg-+-In a- + x +c a 2 ::- l E
  • 24.
    A CQ) Q A+BHJill AuB B A CQ) Q AB HJill AnB B A CQ) Q A-B HJill A B B A CQ) Q A B A H B - co6brrHl!. CaoiicTBa co6hrrHii: l. A+B=B+A 2. (A+B)+C =A+ (B+C) = A+B+C 3. AB=BA 4. (AB)C = A(BC) =ABC 5. A(B+C)=AB+AC P(A)- aepoJITHOCTh crryqaiiHoro co6hITHll A 1. O~P(A)~l 2. BepoJITHOCTh )l;OCToaepHoro co6hrrHll paaHa 1 3. BepoJITHOCTh HeB03MO:lKHoro co6hrrHll paaHa 0 TeopeMLt CJIOllCeuu11 u yMuollCenuH eepoHTHOCTeii. TeopeMa cJIO)KeHHl! aepoJITHOCTeii: P(A+B+ ...+Z) = = P(A)+P(B)+ ...+P(Z), ecJIH co6hITHll He33BHCHMhI. P(A+ B) = P(A)+ P(B)-P(AB), ecJIH co6brrHll 3aBHCHMhI. Cne.LlCTBHe: P(A) = 1- P(A) P(AB..Z) = P(A)P(B)...P(Z) , ecJIH co6hITHll He3aBHCHMhI. P(AB) = P(A)PA(B)+ P(B)P8 (A) (r.le P,._ (B) H P8 (A )-ycnOBHhie aepoJITHOCTH), ec.TH cofihITHJI 33BHClillhl. lfucno pa3MeJ.I.1eHHii H3 n JneMeHTOB no m: A,~ = n(n - l)(n - 2)...(n - m + 1) A;;'= n! (n-m)! lfucno pa3MeJ.I.1eHHii H3 n JJieMeHToB no m CnOBTOpeHHl!MH: A,,m = n! (n-m)! lfucno coqeTaHHii H3 n JJieMeHTOB no m: cm= n(n-l)(n-2)...(n-m+l) n I I m. cm= n. n m!(n-m)! lfucno coqcraHHii H3 n JJieMeHTOB no m CnOBTOpeHHl!MH: c: = c:+m-l Caoiicraa qncna coqeraHHii: c: = c;-m lfucno nepeCTaHOBOK H3 n 3JieMeHTOB: P,, = n! Cl>opMYJia 6HHOMa llilOTOHa: (a +b)" = C~a" + C!a"-1b + c;a"-2b2 + p (A)= P(AB). p (B) = P(AB) B P(B) , A P(A) <l>OPMYJI3 nOJIHOH aepoJITHOCTH: n P(A) = L P(Bk)PB, (A), k=l B1, B2 , ••• , Bn He3aBHCHMhl H o6pa3)'IOT nOJIH)'IO rpyrrny COOhITHH, n T.e. LP(Bk)=l k=l P(Bk)P8 (A) <l>OPMYJia Eaiieca: PA (Bk)= n k 0.5 P(m) 0.4 0.3 0.2 0. 1 p=0.2 LP(Bk)PB, (A) n=5 2 3 p=0.8 4 <l>yHKIUfJI pacrrpe.ZJ;erreHIDI: F(x) =LP(X =x) X;<X P(a s X s b) =F(b)-F(a) n M[X]= LX;P; i=l ~crrepcID1: D[X] =M[(X - M[X])2 ] n D[X] =L(X; -M[X])2 pi i=l D[X] =M[X 2 ]-(M[X])2 Cpe.1U1ee KBa.ZJ;panf'rnoe orKJioHeHHe: ax= -JD[X] b P(a < X <b) =Jf(x)dx, a f (x) - IIJIOTHOCTh aepoHTHOCTH <l>yHKIUfJI pacrrpe.ZJ;eneHIDI: x F(x) = ff(t)dt MareMaTH'ieCKoe OJKII.ZJ;aHHe: -mx =f.xf(x)dx ~crrepcIDI: -Dx = J(x -mx)2 f (x)dx M(X) =np D(X) =npq m5
  • 25.
    BepoHTHOCTh noeJieHIDI co6LITIDIm pa3 s n onurax: Pm,n =c:;pmqn-m(rll.eq =1- p ); Bepo.srraOCTI> noeneHIDI co6hITHJ1 ae Meaee m pa3 s n omrrax: L:P,,.k Bepo.srrHOCTh noeneHIDI co6hrrHll xorn: 6hr 1 pa3 s n omrrax: Hamiepo.srraeKm:ee 'lHCJIO m0 aacrynneHIDI co6hITHll B n omrrax: np-q5,m0 5,np+q 3aKOH pacnpeAeneHM.R nyacCOH8 P(m) 0.5 0.4 0.3 0.2 0.1 2 3 4 5 6 m PaeHOMepHblM38KOH pacnpeAeneHM.R IlJIOTHOCTh pacnpe/1.eJieHIDI: 1 0,x< a f(x)= - 1- ,a$x5,b b-a O,x>b 3ar<oa pacnpeJJ:eJieHIDI: 1 0,x<a x-a F(x)= - - ,a$x5,b b-a 1,x>b HopManbHblM 3aKoH pacnpeAeneHM.R /(x) 1 a.fiii 1 a-J21ie a-a IlJIOTHOCTh BepGJITHOCTH: l _(x- a)2 rpN(x) =--e 2u' a.fiii <l>yHI<IJ;IUI pacnpell.eJieHIDI: 1 1 x-a F (x)= - +- <P(- ) N 2 2 (Y Csoiicrsa: a a+a x M(X)=a D(X) = a 2 1. P(x1 5, X 5, X2) = .!_[<P(Xz - a)-<P(X1 -a)] 2 a a 2. P(IX -al5, ~) = <!>(~) a 3. npaBH..10 ~X CJITY: PQX - al> 3a) = 1- PQX - a 5, 3a) = 1-0.9973 = 0.0027 M(X)=A D(X) =A. M(x) = a+b 2 D(x) =(b-a)2 12 IlorHopManbHoe pacnpeAeneHMe 1 rp(x)= ~ e a-v21lx M(X) =ae 2 (lnx- lna)2 2172 D(X) =a2e172 (e172 -1) noKa3aTenbHOe pacnpeAeneHMe rp(x) =lie-.<x(x > 0) M(X) =~ D(X) = iz PacnpeAeneHMe X2 n z2(n) =LZ;2, i=I rJJ:e Z; HMeroT pacnpeJJ:eJieHlle N(O;l) M[z2 (n)] =n D[z2 (n)] =2n PacnpeAeneHMe CTbtOAeHTa t(n) = z , ~%2(7. rJJ:e z HMeeT pacnpeJJ:eJieHlle N(O;l) M[t(n)] =0 TeopeMa Myaepa-Ilannaca P(a 5, y $ b) "" _![Cf>(b - np) _ Cf>(a - np)] 2 ~npq ~npq l.JaCTKldii: CJl)"lalf: P(np - l $ Y $ np +l) =P(IY - npl < 1) ""Cf>( i:::),-ynpq rJJ:e l = np - a = b - np TeopeMa 4e6b1weea rJJ:e e -CKOJTh yroJJ:HO MaJioe IlOJIOlKKfeJThHoe 'IHCJIO TeopeMa 6epHynnM 11H<PopM84HOHHO-Cnpaao4H8" ra6n•4a © 000 •l1H<Ponnacr-, 2004 r. MocKBB, Kaw•pc•oe wocce, 21 E- maB@nfopas/.ru wwwd:lolastru
  • 26.
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1,65 29 4. 18 3,33 2.93 2.70 2,54 2,43 2,28 2,10 1,90 1,64 30 4,17 3,32 2,92 2,69 2,53 2,42 2,27 2,09 1,89 1,62 35 4, 12 3,26 2.87 2.64 2,48 2,37 2.22 2,04 1,83 1,57 40 4,08 3.23 2.84 2.6 1 2,45 2,34 2,18 2,00 1,79 1.52 45 4.06 3,21 2.81 2,58 2,42 2,3 1 2,15 1.97 1,76 1,48 50 4.03 3,1 8 2.79 2,56 2,40 2,29 2,13 1,95 1.74 1,44 60 4.00 3, 15 2.76 2,52 2,37 2,25 2,10 1,92 l ,70 l,39 70 3,98 3, 13 2.74 2,50 2,35 2.23 2,07 1,89 1,67 l,35 80 3,96 3,ll 2,72 2,49 2.21 2,06 1,88 1,65 1,3 1 90 3.95 3,10 2,7 1 2.47 2,20 2,04 1.86 1,64 1,28 100 3,94 3,09 2,70 2,46 2.30 2.1 9 2,03 1,85 1,63 1,26 125 3,92 3.07 2.68 2.44 2,29 2, 17 2,0 1 1,83 1,60 1,2 1 150 3.90 3,06 2,66 2,43 2,27 2, 16 2,00 1,82 1.59 ,18 200 '3.89 3.04 2.65 2,42 2,26 2,14 1.98 1,80 1,57 1,14 300 3,87 3,03 2.64 2,41 2,25 2, 13 1,97 1,79. 1,55 1,10 400 3.86 3.02 2,63 2,40 2,24 2. 12 1.96 1,78 1.54 1,07 500 3,86 3,01 2.62 2,39 2,23 2. 11 1.96 1.77 1.54 1,06 1000 3,85 3,00 2,61 2,38 2,22 2.10 1,95 1,76 1,53 1,03 - 3.84 2,99 2.60 2,37 2,2 1 2,09 1,94 1,75 1.52 Ta6Jmu:a 3H3 llCHHii tr= t(y, n) KpllTCplUI C TbIO}leHTa 11/r 0,95 0,99 0.999 nly 0,95 0,99 0,999 5 2.78 4,60 8.6 1 20 2,093 2,361 3,883 6 2.57 4,03 6,86 25 2,064 2,797 3,745 7 2,45 3,71 5,96 30 2,045 2,756 3,659 8 2,37 3,50 5,41 35 2.032 2,720 3,600 9 2,31 3,36 5.04 40 2,023 2,708 3,558 10 2,26 3,25 4,78 45 2,016 2,692 3,527 II 2,23 3, 17 4,59 50 2,009 2,679 3,502 12 2,20 3, 11 4,44 60 2,00 1 2,662 3,464 13 2,18 3,06 4,32 70 1,996 2,649 3,439 14 2, 16 3,01 4,22 80 1.001 2,640 3,418 15 2,15 2,98 4, 14 90 1,987 2.633 3,403 16 2.1 3 2,95 4,07 JOO 1,984 2,627 3,392 17 2,12 2,92 4,02 120 1,980 2.617 3.374 18 2,11 2,90 3,97 - 1,960 2,576 3.291 19 2, 10 2.88 3.92 x y 0,00 00000 0,01 0.0040 0.02 0,0080 0,03 0,0120 0,04 0,0160 0,05 0,0 199 0,06 0,0239 0,07 0.0279 0,08 0,0319 0,09 0,0359 0,10 0.0398 0,11 0,0438 0,12 0,0478 x y 0,49 0,1879 0,50 0, 1915 0,51 0, 1950 0,52 0,1985 0,53 0.20!9 0,54 0,2054 0.55 0.2088 0,56 0,2123 0.57 0,2157 0,58 0,2!90 0.59 0.2224 0,60 0,2257 0.61 0.2291 0,62 0,2324 0.63 0.2357 0.64 0,2389 0,65 0.2422 0,66 0,2454 0,67 0.2486 0,68 0,25 17 0.69 0.2549 0,70 0,2580 0,71 0,26 11 0,72 0,2642 0,73 0,2673 0.74 0.2703 0.75 0,2734 0,76 0,2764 0,77 0,2794 0,78 0.2823 0,79 0,2852 0.80 0,2881 0,81 0,2910 0,82 0,2939 0,83 0.2967 0.84 0.2995 0,85 0,3023 0,86 0,3051 0,87 0.3078 0,88 0.3106 0,89 0,3133 0,90 0.3159 0,91 0,3 186 0.92 0,3 112 0,93 0.3238 0,94 0,3264 0,95 0,3289 0,96 0.3315 0,97 0,3340 0,98 0,3365 0,99 0,3389 1.00 0.3413 1.01 0.3438 3naqennH cjlyn1<111111 JlanJiaca I x _.t: y = ll>(x)= - Je 2 dt 5o x y x y x 0.13 0.05 17 0,25 0,()987 0,37 0,14 0,0557 0,26 0,1026 0,38 0,15 0,0596 0,27 0,1064 0,39 0.16 0,0636 0,28 0.1103 0,40 0,17 0,0675 0,29 0,114! 0,41 0,18 0,07 14 0,30 0,1179 0,42 0.19 0,0753 0,31 0.1217 0,43 0.20 0,0793 0,32 0,1255 0.44 0,2 1 0,0832 0,33 0,1293 0,45 0.22 0,0871 0,34 0,1331 0,46 0.23 0,09!0 0,35 0,1368 0,47 0.24 0.0948 0,36 0,1406 0,48 x y x y x 1,02 0,346 1 1,55 0,4394 2,!6 1.03 0.3485 1,56 0.4406 2.18 J.04 0,3508 1,57 0,44 18 2,20 1,05 0,353 1 1,58 0.4429 2.22 1,06 0,3554 1,59 0,444 1 2,24 l,(J7 0,3577 1,60 0,4452 2,26 1,08 0,3599 1,61 0,4463 2.28 1,09 0.3621 1,62 0,4474 2,30 l, 10 0,3643 1,63 0,4484 2,32 1.11 0,3665 1,64 0.4495 2,34 !,12 0,3686 1,65 0.4505 2.36 1.13 0.3708 1,66 0,4515 2,38 l.!4 0,3729 1,67 0,4525 2,40 l.!5 0,3749 1.68 0.4535 2,42 1.16 0.3770 1,69 0,4545 2,44 l.17 0,3790 1,70 0,4554 2.46 1,18 0,3810 1,7 1 0,4564 2.48 1.19 0.3830 1,72 0,4573 2,50 1,20 0,3849 1,73 0,4582 2,52 1.2 1 0,3869 1,74 0,4591 2.54 1,22 0,3888 1.75 0,4599 2,56 1.23 0,3907 J,76 0,4608 2,58 1.24 0,3925 !,77 0,4616 2,60 1.25 0,39 14 1.78 0.4625 2.62 1.26 0,3962 1,79 0,4633 2,64 1.27 0,3980 l.80 0,4641 2,66 1,28 0,3997 1,81 0,4649 2,68 1,29 0,4015 1.82 0,4656 2,70 1,30 0,4032 L.83 0,4664 2,72 1,31 0,4049 1,84 0,467 1 2.74 1,32 0,4066 1,85 0,4678 2,76 1,33 0,4082 1,86 0,4686 2,78 1,34 0,4099 1,87 0,4693 2,80 1,35 0,4115 1.88 0,4699 2,82 1.36 0,4131 1.89 0,4706 2,84 1.37 0.4147 l.90 0,4713 2,86 1,38 0,4162 1,91 0,4719 2,88 1,39 0,4177 1,92 0,4726 2,90 ,40 0,4192 1,93 0,4732 2,92 l.41 0.4207 l,94 0,4738 2,94 1,42 0,4222 1,95 0,4744 2,96 1,43 0,4236 1,96 0,4750 2,98 1,44 0,4251 1,97 0,4756 3.00 1,45 0,4265 1.98 0,476 1 3,20 1.46 0,4279 1,99 0,4767 3,40 1,47 0,4292 2.00 0,4772 3,6-0 1,48 0,4306 2,02 0,4783 3,80 J,49 0,4319 2.04 0,4793 4,00 1,50 0,4332 2,06 0,4803 4.50 1,51 0,4345 2.08 0,4812 5.00 1,52 0,4357 2,10 0,4821 1,53 0,4370 2,12 0,4830 1.54 0.4382 2.14 0,4838 y 0.1443 0,1480 0, 1517 0.1554 0,1 591 0,1628 0, 1664 0. 1700 0,1736 0, 1772 0, 1808 0. 1844 y 0,4846 04854 0,4861 0,4868 0,4875 0.4881 0,4887 0,4893 0,4898 0,4904 0,4908 0,4913 0.4918 0,4922 0,4927 0.4931 0,4934 0,4938 0,494 1 0,4945 0,4948 0,495 1 0.4953 0.4956 0,4959 0.496 1 0,4963 0,4965 0,4967 0,4969 0,4971 0,4973 0.4974 0,4976 0,4977 0,4979 0,4980 0.4981 0.4982 0,4984 0,4985 0,4986 0.49865 0,49931 0,49966 0,499841 0,499928 0.499968 0,499997 0,49999997
  • 27.
    ' 0,0 0, 1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 I.I 1.2 1,3 1.4 1,5 1,6 1,7 1.8 1,9 2.0 2.1 2,2 2.3 2,4 2.5 2.6 2.7 2,8 1.9 0.1 0,2 3Ha'leHllHlj>y HKl.11111 n y aCCOH3 P (A)= A-' e_, k k! 0,3 0,4 0,5 0.6 0.7 0.8 0,9 0,904837 0,818731 0,740818 0,670320 0,60653! 0,548812 0,496585 0,449329 0,406570 0,090484 0,163746 0,222245 0,268128 0,303265 0,329287 0,347610 0,359463 0,3659!3 0,004524 0,016375 0,033337 0,053626 0,075816 0,098786 0. 121663 0, 143785 0,16466 1 0,000151 0,00 109 1 0,003334 0.007150 0.012636 0,019757 0,028388 0,038343 0,049398 0,000004 0,000055 0,000250 0,000715 0,00!580 0,002964 0.004968 0,007669 0,011115 1,0 0,000002 0,000015 0,000057 0,000158 0,000356 0,000695 0,001227 0,002001 OJJOOOOI 0.000004 OJJOOOl3 0,000035 0,000081 U,000 164 0,000300 0,000001 0.000003 0.000008 0,000019 0,000039 0.000002 0,000004 2,0 3.0 4,0 5.0 6.0 7,0 8,0 9,0 0,367879 0.135335 0,049787 0,018316 0,006738 0.002479 0,000912 0J)00335 0,000123 0,367879 0,270671 0, 149361 0,073263 0,033690 0,014873 0,006383 0.002684 OJJOl l 11 0,183940 0.27067 1 0,224042 0,146525 0.084224 0.04468 0.02234! 0.0 10735 0,004998 0,061313 0. 180447 0,224042 0, 195367 0,140374 0,089235 0.052129 0,028626 0.014994 0.015328 0.090224 0,168031 0. 195367 0, 175467 0,133853 0.091226 0.057252 0.033737 0,003066 0,036089 0,1008 19 0,156293 0,175467 0,160623 0,1277 17 0,091604 0,060727 0,00051 1 0,01 2030 0.050409 0,104194 0,146213 0, 160613 0,149003 0.122138 0,09 10'Xl 0.000073 0.003437 0,02 1604 0.059540 0, 104445 0.1 37677 0.149003 0,139587 O. l 17 l 16 0,000009 0,000859 0.008!01 0,029770 0,065278 0.103258 0,130377 0.139587 0.13 1756 0,000001 0,000191 0.00270 1 0,013231 0,036266 0,068838 0,101405 0,124007 0.131756 10 0.()00038 0.()00810 0.005292 0.018 133 0,041303 0.070983 0.099262 0, 11 8580 0,000007 0,000221 0.001925 0.008242 0,022529 0,045!71 0,072190 0.097020 12 OJ){)()()OI 0.000055 0.000642 0,003434 0.0 11262 0,026350 0.048127 0.072765 13 0,000013 0,000197 0.001321 0,005199 0.0 14 188 0.0296 16 0,050376 14 0,()()()0(}3 0,000056 0.000472 0,002228 0,007094 0,0 16924 0,032384 15 16 17 18 19 20 21 22 23 24 25 26 27 0 I 2 O,OOOClO! 0,000015 0.000157 0,000891 0,00331 I 0.009026 0,019431 0,000004 0,000049 0,000334 0.001448 0.004513 0,010930 0,000001 0,000014 0,000118 0,000596 0.002124 0.005786 0,000004 0,000039 0,000232 0,000944 0,002893 0.000001 OJJ000t2 0,000085 0.000397 0.001370 0,000004 0,000030 0,000159 0,000617 3 4 5 6 0.000001 0,000010 0,000061 0,000264 0.000003 0,000022 0,000108 0.00000! 0,000008 0,000042 0,000003 0,000016 7 8 0,000001 0,000006 9 0,000002 0,000001 311aqe11nn t -1<p1nep1111 C ThlOllCHTa 11p11 ypoBHe 3113'1HMOCTll 0,10; 0,05; 0,01 (1111yxcTOpOH111ttt) I.f.Hc.no cTeneHeH a CBOfiO)J;hl d._f. 0, 10 0,05 O,Ql 1 6,3 138 12,706 63,657 2 2,9200 4,3027 9,9248 3 2,3534 3, 1825 5,8409 4 2, 1318 2,7764 4,604 1 5 2,0150 2,5706 4,0321 6 1,9432 2,4469 3,7074 7 1,8946 2,3646 3,4995 8 1,8595 2,3060 3,3554 9 1,833 1 2,2622 3,2498 IO 1,8 125 2,228 1 3, 1693 I I 1,7959 2,20 10 3,1058 12 1,7823 2, 1788 3,0545 13 1,7709 2, 1604 3,01 23 14 1,761 3 2, 1448 2,9768 15 1,7530 2,1315 2,9467 16 1,7459 2,1199, 2,9208 17 1,7396 2, 1098 2,8982 18 1,7341 2, 1009 2,8784 19 1,7291 2,0930 2,8609 20 1,7247 2,0860 2,8453 21 1,7207 2,0796 2,8314 22 1,7 17 1 2,0739 2,8188 23 1,7139 2,0687 2,8073 24 1,7109 2,0639 2,7969 25 1,7081 2,0595 2,7874 26 1,7056 2,0555 2,7787 27 1,7033 2,0518 2,7707 28 1,701 1 2,0484 2,7633 29 1,6991 2,0452 2,7564 30 1,6973 2,0423 2,7500 40 1,6839 2,021 1 2,7045 60 1,6707 2,0003 2,6603 120 1,6577 1,9799 2,6174 ~ 1,6449 1,9600 2,5758 0,3989 3989 3989 3988 39986 3984 0,3970 3965 3961 3956 3951 3945 3982 3980 3977 3939 3932 3925 3973 3918 3ttaqeHHH <l>YHKQHH 1 _£ <p(x) = ~-e 2 5ff0,3910 3902 3894 3885 3876 3867 3857 3847 3836 3825 0,3814 3802 3790 3778 3765 3752 3739 3726 3712 3697 0,3683 3668 3653 3637 362 1 3605 3589 3572 3555 3538 0,3521 3503 3485 3467 3448 3429 3410 3391 3372 3352 ' 0 I 2 3 4 5 6 7 8 9 0,3332 3312 3292 3271 325 1 3230 3209 3!87 3166 3144 3,0 0,0044 0043 0042 0040 0039 0038 0037 ·. 0036 0035 0034 0,3123 3101 3079 3056 3034 3011 2989 2966 2943 2920 3.1 0,0033 0032 0031 0030 0029 0028 0027 0026 0025 0025 0,2897 2874 2850 2827 2803 2780 2756 2732 2709 2685 3,2 0,0024 0023 0022 0022 0021 0020 0020 0019 0018 0018 0,2661 2637 2613 2589 2565 2541 2516 2492 2468 2444 3,3 0,0017 0017 00 16 00 16 0015 00l5 0014 0014 00 13 0013 0,2420 2396 2371 2347 2323 2299 2275 225 1 2227 2203 0,2 179 2 155 213 1 2107 2083 2059 2036 20 1?. 1989 1965 3.4 0,0012 0012 0012 0011 0011 001 0 00 10 0010 0009 0009 3.5 0,0009 0008 0008 0008 0008 0007 0007 0007 0007 0006 3,6 0,0006 0006 0006 0005 0005 0005 0005 0005 0005 0004 0,1942 1919 1895 1872 1849 1826 1804 178 1 1758 1736 3,7 0.0004 0004 0004 0004 0004 0004 0003 0003 0003 0003 0,1714 169 1 1669 1647 1626 1604 1582 1561 1539 1518 3,8 0.0003 0003 0003 0003 0003 0002 0002 0002 0002 0002 0.1497 1476 1456 1435 1415 1394 1374 1354 1334 1315 0,1295 1276 1257 1238 1219 1200 1182 1163 Jl45 1127 3,9 0,0002 0002 0002 0002 0002 0002 0002 0002 0001 000 1 O,t 109 1092 1074 1057 1040 1023 1006 0989 0973 0957 0,0940 0925 0909 0893 0878 0863 0848 0833 08 18 0804 0,0790 0775 0761 0748 0734 0721 0707 0694 0681 0669 0.0656 0644 0632 0620 0008 0596 0584 0573 0562 055! 0,0540 0529 0519 0508 0498 0488 0478 0468 0459 0449 0,0440 0431 0422 0413 0404 0396 0387 0379 0371 0363 0,0355 0347 0339 0332 0325 0317 0310 0303 0297 0290 0,0283 0277 0270 0264 0258 0252 0246 0241 0235 0229 0,0224 02 19 02!3 0208 0203 0198 0194 0189 0 184 0180 0,0175 0171 01 67 0163 0158 0154 015 1 0147 0143 0139 0,0136 0!32 0 129 0126 0122 01 19 0116 01 13 OllO 0107 0.0!04 0 !01 0099 0096 0093 0091 0088 0086 0084 0081 0,0079 0077 0075 0073 0071 0069 0067 0065 0063 0061 0.0060 0058 0056 0055 0053 0051 0050 IJO.lS IJO.l7 IJO.l6
  • 28.
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(..13 pacnnasa OAHOBpeMeHHO Bb1A€fll'1flli1Cb ra3bl Lil napbl BOAbl, KOTOpble cQJopML11pOB811Lil aT- MOCQJepy Lil r1'1Ap0c¢epy. Q Me3030i1CK8R («CP8AH5l5l :>Kl-13Hb») - OT 225-230 AO 65-67 MJlH. neT H83a,q 0 KaMH030i1CKBR («HOBafl >f<.13Hb») - OT 65-67 MJlH. neT Ha3aA 8HyTpl'1 3p Bb1A911fllOTC>l MeHbWl!le spe- MeHHble 0Tpe3Klil - nepLllOAbl. /h.noccpepa - Tsepga5l 060- flO'-l Ka 3eMnlil, BKn10'-l810ll.la5l sepXHIOIO '-l8CTb, M8HH1Lil l'1 3eM- HYIO Kopy, COCT05lll.IYIO 1'13 Tsep- AblX Mlt1Hepanos l'1 ropHblX nopog. Cyll.leCTBYIOT gsa BLilAa 3eM- HOCi KOpbl: MaTepHKOBBR H OKeaHH'"leCKaR . nopOAbl, CJlaralOIJ.He 3eMHYIO KOpy no cnoco6y 06pa3osaH1-1s:i pa3nlil'-lalOT: 1. MarMarn'-leCKMe nopOAbl. 06pa3ylOTCS'I npl'1 1'13Bep)f<eHi..1111 MarMbl lt13 rny61-1HHblX 30H 3eMJ1Lil l'1 ee 38TBepgeHl'1Lil. a) rny61'1HHble (rpaHllT, ra6po); 6) 1t13111-1swL11eC5l (6a3anbT, ,q111a6a3, neM3a). 2. OcaAO'-IHble nopOAbl. 06pa3ylOTCS'I TOJlbKO Ha nosepXHOCT1'1 3€M- HOVi KOpbl n1-160 3a C'-leT ,qes:iTeflbHOCT1'1 opraHl'13MOB, n11160 np1'1 pa3pywe- Hl'1lt1 ropHblX nopOA, n1-160 3a C'-leT Xl'1Ml'1'-l€CK1'1X peaK41-1Lli. a) 06noMO'-lHb1e (necYaHl'1K, necoK, rn1-1Ha, ranbKa, rpas1t1il1); 6) opraH111'-leCKL11e (Men, 1113secrns:1K, Top¢, yronb); a) x1-1ML11'-lecK111e (Kan1-1VIHb1e con1-1, nosapeHHble con1i1) . 3. MeTaMopcf>w-1ecK1o1e nopOAbL ropHble nopo,qb1, npeTepneswllle 1'13MeHeHLllfl no,q ,qeeiCTBLlleM ,qasneHLllS'I Lii BblCOKLllX TeMnepaTyp, B pe- 3YllbTaTe onyCK8Hl'15l yYaCTKa 3eMHOCi KOpb1 (MpaMop, rHeeic, Ksap4l'1T). MaTepl'1Kl'1, BKnl048fl no,qBOAHble 0Kp8111Hbl, Lil OK98Hbl >lBflfllOTC>l ca- MblMLll KpynHblMLll CTpyKTYPHblMl'1 3neMeHT8M.1 39MHOVi KOpbl. B 111X npe,qe- nax OCHOBH85l nnOL1.18Ab npLllH8Afl9:>Kl'1T cnoKOCiHblM nnaTQ.JOpMeHHblM y'-laCTKaM, MeHbW8>l - no,qBl'1)f<HblM reOClt1HKJ1111H8JlflM. reoCHHK.mtH8fll'1 - o6wlilpHble no,qBl'1>KHble y'-laCTK.1 36MHOCi KOpbl, c1-1nbHO pacYneHeHHb1e, c pa3Hoo6pa3HblMLll TeKTOH1'1YeCKLllMLll ,qs1-1>1<eH1i1s:iMi'!. .. .... Penbecp 3eMJllil - COBOKynHOCTb HepOBHOCTeVI 39MHOVi nosepxHocrn. npolecC BHy1peHH11l1 (3HAOreHHbll1) BHewH11l1 (3K3or€HHbl ~) BHeWHMe (3K30reHHble) npo4eCCbl BHyrpeHH/lle (3HAOreHHb1€) npo4ecCbl npw·n1Ha AesnenbHOCTb Pe3yl1bTaT ABl1JKeH11>1, o6pa3yKJTCH Bb1CTynb1 MaTep11KOB, BHyTpeHHHHTennora BeprnKanbHblenepeMe· snaA11HblOKeaHOB, 3eMn11 U€Hl1H, rop1130HTaflbHbl€ ropHb1eo6nacrn, AB11JKeHl1H paBHl1Hbl. (n111oc¢iepHblX nn11T) 3Heprn>i ConHLa , c11na pa3pyweH11>111 BblpaBHl1Ba1-111e TH)l(€CTl1,BblB€Tpl-1· pa3pyweH11e ropHblX penbe¢a BaH11>1:¢1131-14eGKOe, X11Ml14€CKO€, pa601a nopoA, nepeHoc $opM11posaH11e MaTep11ana, orno)l(eH11e HOBblX¢lOpM T€K)''ll1X BOA, no1:13eM- MaTep11ana11ero penbetj:ia: MOP€Hbl, HbleBOAbl,fl€AH11K11, K3Mbl,03bl, MOpCKO~ np1160~, ,Qes:I- «6apa Hb11n6b1» 11 T€flbHOCTb'l€f108€K3. T.A. nnaTq>OpMbl - ,qpe0HeViw111e OTHOCl!ITeJlbHO ycTOVi4111Bble Lil BblpOB- HeHHble yyacTKl'1 3eMHOCi KOpb1. Ha 3eMne 9 nnaT¢OpM: 1. Cesepo-aMepl'1KaHcKa>l 2. BocTO'-lHO-esponeeicKas:i 3. C1-161-1pcKas:1 4. IO:>t<HO-aMep111KaHcKas:i 5. A¢p1i1KaHo-apas1i1VicK85I 6. lllHAOCTaHCKafl 7. ABCTpa111t1iliCK8s:I 8. AHTapKTLll'-lSCK85l 9. K1i1rneicKa>l Bt>XD/1 <IJYHAaMe•-na HanoaepXHOGTb npOMCXO>K.qeHM.e MBTepM.KOB M OKeaHOB MaTepL11KOB8fl Iii OK88HVl'-leCK8s:I 3SMH8fl KOpa: M06MnbH8 (Ha OCHOBe rl'1nOT€3bl A. BereHepa - 1912 r., H€M8LKVli"ii reoQJV131'1K) TeopMs:! fllltTOCQlepHblX OflMT 1. Ceeepo-aMepuKaHcKaR 5. V11./:loaecrpan11McKaR 2. IOJKHO-aMepuKaHcKaR 6. AHrapKrw--1ecKaR 3. Eepa3ui1cKaR 7. f MXOOK68HCK8R 4. AcjJpuKaHCKaR nepeMSLl.18IOTCfl co CKOpOCTblO OT 1 AO 6 CM OT Jll!IHLllLll nOABOAHb1X xpe6TOB K JllilHl'1s:IM :>Ke1106os. C6n111:>Kat0TCS'I, CM1'1H8IOTC5l B CKna,qKJ.1, ropHble o6naCT1'1. 0KeaHV1'-leCK8>l KOpa «Hblp5l9T» no,q KOHTVIH8HT8JlbHYIO, npVI 3TOM o6pa3ylOTC5l rny60KOBOAHb1e :>t<eno6a, oCTposHb1e gyrn, ropHb1e xpe6Tbl. CeeicM1-1YeCKL11e nos:1ca 3eMnl'1 - norpaHl'14Hb1e o6nacrn M9*AY 111i1TOc¢epHblML11 nn1-1rnM1t1 (95% 3eM11eTp5lceH111Vi, sy11KaHL113M). OcHOBHb1e cj>opMa penbecpa PaBHLi!Hbl - 06w111pHble yYaCTKl'1 3SMHOCi nosepxHOCT1'1 c M81lblM (AO 200 MeTpos) Kone6aHLll8M BblCOT. B TeKTOHLllY€CKOM OTHOW9Hlt1VI OHLll COOTBeTCT- BYIOT YCTOCi'-lLllBblM nnaTQ.JOpMaM. Pa3111'1'-ll'1e pasHVIH no BblCOTe ropbl - 3TO BbinyK11as:1 Q.JopMa penbeQ.Ja c xopowo sb1pa:>t<eHHoill aepw111H0Vi, nOAOWBOVi, CKJlOHaMLll. An1i1Ha rap COTHl'1, TblCS'l'-11'1 KVlnoMeTpos, BblCOTa - AO HeCKOJlbKVIX Kl'1JlOMeTpOB. ropHble CTP8Hbl COCT01'1T 1113 OTASflbHblX ropHblX xpe6TOB Lii pa3Aefls:llOL1.11-1X 1'1X AOflLllH l'1 KOTflOBl'1H. 8b1corn rop: 0 HM3KMe - AO 1000 M (CpeAH1'1Ci Ypan) 0 cpep,HeBb/COTHb/e - 1000-2000 M (KapnaTbl) 0 Bb/COK/lle - 2000 M (T>lHb-WaHb, rLllM8118Lll) "'Pw""'=iiitCKllOH llO,lOllJD3
  • 29.
    Ae~o+ceHHSI aeMHO~ KOpb1 ATMOCcj>epa 1.rop1113oHTallbHOe - 06pa3yeT CK11ap,K111, nporn6b1 2. BepT111Ka!lbHOe - (cM. p111c.) ATMOct1Jepa - ra3oo6pa3Hafl 060110'-!Ka 3eMnlil. 3Ha"lem1e: 3eM11eTpswceHHS1 O Ab1XaH111e; «CellicMO!lOfl/151» - OT «CellicMOC» - 3eM!leTps:!CeH.fe. Cei1cMw1ecKne noRca - norpaHLil4Hble o6nacTM Me>KAY 1111Toc¢ep- 0 3al.lll..fTa OT KOCMW-·19CKlilX l.f311Y49Hl.1'1 ..., oxna>KA9Hl.1e 39MHOlli noaepXHOCTl.1; 0 nctAeH1i1e MeTeop1.nos; 0 06pa3osaH1i1e o6naKoB, AO>K.As:!, cHera, seTpa.HblMltl nmHaMltl. 0"18( JeMneTpRCeHUR - Ha rny6li1He, MeCTO pa3pb1Ba lil CMew.eHlil51 nopoA. 3nH4eHrp - Ha nosepXHOCTlil, Hap, OYaroM. 1970 r. n epy - 9-10 6annoa 1960 r. 41-1111.1-10- 11 6am1os COCTBB 803.qyxa 1. A30T - 78,8% 2. K1i1c11opoA - 20,95% 3. C02 - 0,03 % 4. V1HepTHble ra3bL - 0,94% 5. BoA51HOlli nap, np1.1Mec1i1 {nbl!lb, cepHlilCTblYI ra3, aMMLilaK) - MeHee 0,01 % lei13epbl - QJOHTaHlllPYIOLll.10 lilCTOYHlllKlil rop511.1ellr BOAbl (KaM'-laTKa). TeMnepaTypa B03Ayxa 3aBlllClilT OT yrna naAeHl-151 CO!lHe'-!HblX ny1.1ellr Ha 30MHYIO noaepxHOCTb. YeM 6!ll.1)K8 K 3KBaropy, TeM 60JlbWe yron naAeHl.151 CO!lH9'-IHblX nyYei::i, C118AOBaTe!lbHO, Cl.1JlbHee HarpeeaeTCSI TepplilTOpl.151, BblWe TeMneparypa np1113eMHoro c11051 aTMocQJepbt (+25°C +26°C). Ha1116011ee Hlll3Kl.1e TeMnepaTypbl - B no- m1pHblX 0611acrsix. lqqOB8$1 aMnJH1TYAB Kone6aHl1R reMneparyp - pa3HOCTb M8)1(AY CPSAHei::i TeMnepaTypolli caMoro Tennoro Iii CaMOro XO!lO,QHOro Mecs:14a B fOAY· CyTO'-IHBR aMnnHTy,qa Kone6amm TeMneparyp - pa3HOCTb MS)KAY C8MOlli BblCOKOlli l.1 caMoi::i Hl.13KOC1 TeMnepaTypoi::i B T8'-18Hlil8 CYTOK. Berep - ABLil)K8Hl.1e B03AYX8 B roplil30HT8JlbHOM HanpaeneHlillil. npl-1'-11.fHB : pa3HOCTb B aTMOCQ:>epHOM ,qaaneHlilltl Ha,q p83HblM.1 y1.1aCTK8Mlll no,qcrn11a10t4ei::i noeepXHOCT.1. BeTep, MSHS110W.Li1H ceoe Hanpae11eH1.1e ,qea pa3a a CyTK1.1, 758 1ss 159 Ha3blBalOT 6pM30M. ~MMr,CT. ~~M~.CT- <l>eH - c ropb1 a ,qo111i1Hbl (KaeKa3, Anbnbt) _....6P<I~ - - ~ MyccoHbl - eer pbl, MeHs:1iow.11e HanpaeneH1-1e no ce30HaM: nernM - c oKeaHa Ha cywy, 3.1MOC1 - c cyw.., Ha oKeaH. CTOKOBble eeTpbl - pacnpocrpaHeHbl B AHrapKT1i1Ae (or 4eHrpa K nep111¢iep1.111). 3Ha'ieHHe eeTpa: O nepeHOC51T Tenno 1o1 enary a rny6b MaTep1.1Ka, ¢lopM1.1py10T KJ11i1Mar; 0 o6pa3oeaH1.1e OKeaH.1'-10CK.1X TeYeH.1171 (nOCTO.l'IHHble aerpb1); O 1.1cno11bJOBaH111e 1.1enoeeKOM (eeTp. M0!1bH1-14b1, napyCHb1e cyAa, no11r1eH1i1e s11eKrpw-1ecrsa); 0 npW-1.1H8 6eACTBlililr (pa3pyweH.1e yparaHaM.1, WTOpMbl). Knli!M8T - MH0f0Jl9TH.1i1 P9)1(l!IMnoro,Qbl, xapaKTepHblYr AJ151 ABHHOYr MSCTHOCTlll. 06118..AaeT ycroi11.11i1so- CTblO .1 nocTOflHCTBOM, XOTfl e>+<erOAHO 6blBalOT 0TKJ10H€H.1fl TeMneparyp, K011.1'-18CTBa Ill pe>+<111Ma OCCAKOB. V1311yYeH1o1e ConH4eM renna 1.1 csera H83b10aercs:1 COflH0"1HOH paA...84..,elil .., lil3Meps:1eTCfl B KLiJlOKa11op1o1six Ha KB. C8HT.1M0TP (KKanlcM2) 39MHOi1 nosepXHOCT.1. 06Ulee KOJ1.1'-18CTBO COJ1H8'-IHOi1 3Heprnlil, AOCT1o1ra10- w.eM nosepxHOCT1i1 3eMJ1Lil, HaJb1eaer cs:1 cyMMapHolil pa- AMa4..,eM. 60llbWOe BJlliSIHLile Ha ¢opMlilpoB8Hlile KJlliMaTa OKa- 3blBaer 3TMOC<tJepH8ff 4MPKYflff4MSI - 38KOHOMepHoe nepeM8UJ.8Hlil0 B03AYWHblX Mace, B npo4ecce KOTOporo npo1-1cxo,q1i1r nepeMeUJ.eH111e Tenna 1-1 enarn Me>Kp,y Ma- rep11K8Mlil Ill OKeaHaM.1. KmnAaroo6pa3y10L11He ci>aKTopbl I I I8blCOTa CollHl.IB n OJlCHIJlalOUBSI Ha,Q ropH30HTOMl / nosepXHOCTb l ~·~'"~ / I803,QywHbl)( MBCC l I Cywa, oKeaH, 3otianbHoepa3J'IH'IHe Ol(eaHw.+ec1ut eTe<1eHHS1, re,.,meparyp ne.aH1tKM, CHera, penbecfl BepT1tKa1lbHOO ABHllCBHHe BOJAYll.a, nocTOSIHHble eerpbl , Myc<:OHbl 803,qyWHble MBCCbl (BM) - 3TO 6oJlbWOlli 06b8M 803,qyxa, 0611a,qa10lJ.1"1C1 OTHOCLilT9JlbHO OAHOpo,q- HblM11 CBO~CTBaML-1 .., ABl.f>KYLJ."1C1C51 K8K CAHO 4enoe. Ha 3eMne Bb1A0115llOT C118AIOLJ.lil8 BM: 0 3KB8TOp118flbHb/0 (3B): T8nflbl8, BJ18)KHbl0 B T040H.10 ro,qa 0 TpOm1'10CKne (TB): MOpCKMe (TM) .1 KOHTMH0HTanbHbl0 (KT) - cyx1-1e, Tenllble 0 yMepeHHb/0 {YB): MOpCKMe (YMB) - Jl€TOM - XOJlOAHble, BJla)KHble, 3L'1MOC1 - Bfl8)KHbl8, renllble .1 K0HTl1H0HTanbHbl0 (YKB) - M8H.l'llOTC51 no C030H8M ro,qa 0 nonRpHaR (nB): apKTl'1'-10CK8R (nAB), aHrapKTl1'-10CK8R (n AB) - cyxafl, X0110AH851 n p1-1 nepeM8LJ.8Hlil.1 BM HaA TOi1 .111.1 .1HOi1 Tepp1.1Top1i1ei1 OH.1 cnoco6Hbl nocTeneHHO .13M8H51Tb CBOl-1 CBOc::iCTBa, T.e. rpaHCQ:>OpM14POB3TbCSI. AB nonoce, p83A81151IOLJ.8Yt pa3Jl.14Hbl0 no CBOlllM ceollicTB8M BM, o6pa3ylOTCSI nepeXOAHblB o6nacrn - aTMoct1JepHble cf>pOHTbl (Tennbllli Ill XOJ10AHbllli) .1 B03HlllK8IOT KpynHble aTMOCQ:>epHble BLi!Xpt.1. L.IHKflOHbl nacMypHaR noro,qa, Bbma,qa/OT OC8,£JKM AHTH4HKflOHbl neTOM - JKapKaR, 314MOH - xono,qHaR JKBaTOp1oianbHb1M 3marop11anbHb1e y araaropa sb1co1Me ret.11eparypt:.1, 6onbl.Uasi enaJKHOCTh cyfoKBaTOpM811bHbl~ 3KBaTopllaObHble II TJXlflll'leCl!lie Mel!(Jl.Y TpOl"lll'leCl!liM II neTo llrapl<Oe, BOBllO-IOe, 311Ma Tenna>i II cyxa>i 3KBaTOp~anbHblM OOSICBM~ rponH~t::ll~ Tpon14 4eCt::le 5nK3TponMKOB t!iblOOKleTemepaTYPbl,CyxOCTb B03i:zyxa cy6TJXlflH'«Kl1~ rponM4ecK11e ~ yMepeHHble we~ r ponll'leCt::llM 11 nero *BpKoe, cyxoe, 3~Ma rennaSI 14 ena*HaR yMepeHHblM yMepeHHbl~ yMepeHHble B yMepeHHblX w11pornx 4eTKO t!iblPaJKeHbl epeMeHa roAa apKT~4ect::11~ apKT114ecK11e 6n113 ceaepHoro nomoca H~3K11e TeMneparypbi, Mano OC<l,QKOB aHTaplCT144eCK11K aHTaplCTM11€Clllie 6n113 IOJKHorO nomoca Hl3K4e TeMnepaTypt.1, Mano OCa,QKOB cy6aplCT14'!eCl!liK yuepeHHble 14 aplCTM~KMe Me'Jt'.IJ;fYMepetttlblM II Hl4 3KHe Te!.tlepBTypbl, Mano OC<!AK08 apm'IOClllM lpyfJ'lbliro,!l cy6atm~m'IElC1111K yMep01M>1el!aHTapm1'!E!CIO!e lleXJJ,'Jywepetff>IMM HMlD!eT~. uaro~ 111¥"".'.'Si ma CTpoeHMe aTMocct>epbt 1. Tponoccpep a (8- 10 KM y no1110cos, 16- 18 KM y 3KBaTopa) - H.1>KH1.1ili cnoVi. Co,qep)l(1t1T 80% so3,qyxa 1.1 90%, BOAs:!Horo napa. 2. Crparoccpepa (50- 55 KM) - noeb1weHo co,qep>KaHL19 030Ha. BOA51HOC1 nap OTCYTCTByeT. 3. Me3occpepa (80- 85 KM} - CflO)KHble npo- 4eccb1nplilBOAs:!T K CB0'-10Hi.110 aTMOC¢epb1. 4. TepMoccpepa (800 KM) - B03AYX .1QHL13L1- poBaH. TeMneparypa Ha BblCOTe 300 KM - 1200°C. 5. 3K3occpepa - reMneparypa ,qo +2500°C ATMOCci>epHOe AaBflSHMe - c1111a, c KO- TOpolii 003,qyx AaB..,T Ha 38MHYIO noeepxHOCTb, Ha ace HaXOA51UJ.Lil0C~ Ha Hei::i npeAM8Tbl. Vfa- Mep~eTCSI np1i16opOM 6apOM8TpoM {«6apoc» - rn.lKeCTb, «MSTP" - Mepa). Asa 0111,qa 6apoMeTpa: PTYTHb1ilr 1-1 anepo1-1,q. HopManbHOe arMocQJepHoe ,qasneH11te - 760 MM.pT.CT., 762 - nOBblWSHHOe, 758 - no- Hlit>K8HHOe. BoAJlHOi< nap a aTMocct>epe nocTynaeT np111 11cnapeH1o1111, KOTopoe npm1CXOA1-1T noCTOs:IHHO B 1110600 epeM.l'I ro,qa KaK c nosepxHOCTl.1 OKeaHa, TaK lit c nosepx- HOCT.1 cyw111, peK, BOA00MOB. vtcnapSllOT BOAY CHer, 118A, a T8K>K9 paCTSHLil~. Ko111i1YeCTBO BOA~Horo napa e rpaMMax , co,qep)Kal!leecsi B 1 M3 B03AYX8, Ha3blBalOT a6co1110THOM ena>KHOCTbto 003,qyxa. B03AYX, KOTOpbltl H0 MO>KeT BM9CTLiTb 60flbW€ BOASIHOrO napa, Y8M OH y>t<e COA€P- .lKLilT, Ha3t-:aatOT H8Cblll8HHblM. B03AYX, KOTOpbllii COAeP)KlllT BOA~Horo napa MSHbWe, '-ISM Mor COABP)l(8Tb, H83bl88- IOT HeHaCblll.18HHblM. 0THOW8Hli8 KOfllit48CTBa .1M8IOUSi::ics:1 B B03AYX9 enarn K TOMY KOJ1.1'-10CTBy, KOTOpoe OH M0)1(0T COA8P>t<8Tb npl.1 ,qaHHOc::i T8Mnepa- TYP8, Ha3b1B8KlT OTHOCLilT8flbHOl4 Bfl 8>KHO- CTblO. B03AYX, l.1M0IOUJ.litlli Bfla)KHQCTb 30% .1 M9HbW0 - cyxoM. B HaCblUJ.eHHOM B03AYX€ OTHOClilT8flbHa~ ena>KHOCTb - 100%. 06naKa 06naKa - cKonneHlil8 BO,qs:!HblX KaneneK e so3,qyxe. 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  • 30.
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"1CT"1HHS5l r eOMBTPlo1Y0CK85l ¢11rypa 3eMJ1"1 6bl118 H3383Ha reoH,qOM (38MJle- noA06HblM). r eo1t1A onpeAenRBTC51 KSK ¢lllrypa, noeep x - HOCTb KOTOpoH BCIOAY nepneHAllKYlls:!pHa Hanpa- BJlBHi.tto Ci.1Jlbl T5l>KBCTlt1, T.e. OTB8CHOili Jllt1Hlt1"1. noeepXHOCTb reo1-1Aa COB08A88T c ypoBHBHHOH noeepXHOCTblO OK03Ha. noAHS'lTHSl II onyCK8Hi.1SI reDl'Aa Ha,q ccpep011AOM COCTSBJls:llOT ±50 AO ±100 M. Pa3HH 48 M0>KAY c¢epOlt1AOM "1 re0"1A0M H0- B8ll11Ka, no3TOMY ,qnR reoAe31-1YecK111x 1-1 Kaprn- rpa¢1o1YeCK1o1x pa6oT e Haweili cTpaHe np.1Hi:!Tbl CJlBAYIOLl.l'le B0Jllt1YHHbl: Q 3KB8TOp113JlbHblVi pa,q.1yC 8=6378,2 KM 0 no.nsipHblili pa,q1o1yc p = 6356,8 KM 0 AJl HHa 3KBaTopa - 4007 5 ,7 KM Q Ol10ll.a,qb 3eMJli.1 = 510 MJlH. KM2 o AflMHa MBPMAM3Ha = 40008,5 KM 6 - CMyrn asi KOJKa, n Mble l-1 TBMHble BOJlOCbl "4<0JlT088TaSI 1-tJllll Kp8CHOB8T8SI l(OJKa, '10pHble npHMble BOJlOCbl, YJKHH paape3 rnaa, BblCT)'T18IOl1Me Cl(ym.i TeMHaR KO>Ka , '!epHble i<yp'laBble aonocb1, TOilCTbl0 ry6b1, WHPOKHH HOC TeMH8R KO>K8, "40pHbl0 KYP'l3Bbl0 HJlH BOJlHHCTble BOJlOCbl, TOJlCTbJB ry6bl, WltpDKMil HOC MynaTbl, Merncb1, caM6o ct>opMa lt1 pa3M9pb1 3eMJl lt1 lt1M0IOT 60.nbWOe reorpacflw.;ecKoe 3HaYeH1-1e. Wapoo6pa3HaR ¢11- rypa 3eM1111 06ycnaa.n11eaer yMeHbWeH1t1e yrna n8A0Hl1fl COJlHB'-IHblX nyyei./i Ha 30MHYIO noeepx- HOCTb OT 3KB8TOpa K nontoeaM ~ o6pa30B8H110 Ten nOBblX noflCOB. Tenn oeble nosica , H8P5!AY c APYH1M.1 ¢aKTO- paM1o1 (pa3M0pbl Ill Macca 3eM1111, paCCTOSIHl-18 OT 3eMJllll AO COflH43) o6ycnaenlllBSIOT 38KOHOMep- Hoe 113MBH0Hlt1B np11poAHblX npOLBCCOB .1 flB/1BH"1Vi s reorpa¢.1YecKoi.ii o6onOYKB no HanpasneH11to OT 3KBaTopa K 0011IOC8M. Pa3M8pbl II Macca 3eMJ1H npBAOnpeA8I15llOT TaKylO c1-1ny npHTSl)f(0Hi.1Sl, KO- TOpa5l YA8P>+<1-1eaeT aTMoc¢epy II r1-1,qpoc¢epy, 683 KOT0pb1X H0803M0)f(H8 )f(lt13Hb. 113,qarenb 000 «l1Hcponnacr ,, Or,qen npo,qa>K: Ten.: (095) 230- 0608109. cjJaKC: (095) 230- 7111, e--maif:maim infoplast.ru. hNp:llwww.infoplast.ru CepnR ..Q6pa30BBHne" no~cepni:i ..reorpacjJnR,. Bt>1nyc1e. 2 ----~ = N ::: = ~----~
  • 32.
    l. IlpOH.3BOJJbHbIH TJJeyrOJJblUiK c>b~y> ~ ~C)'M;-..ia yrnoe TJJeyrOJJhHHKa a+~+y= 180° BttewttHH yroJJ 'IpeyroJJ&HHKa b=a+~ TeopeMa KOCllHYCOB b2 = a2 + c2 - 2ac cos ~ TeopeMa CHH)'COB _a_=_b_ =_c_= 2R sin a sin ~ sin y (zoe R - paouyconucaH1wu 0Kpy:J1CHocmu). ~S =2-ah 2 a l . P. S=-acsml"' 2 S = ~p(p - aXp-bAfJ - c), a+b+c zoe n011ynepw.•emp p = 2 l(eHTJl OilHCaHHOH OKpy11rnoc- TH - TOqKa nepece4eHllJI cepe- .llHHllblX nepneH,llHKYJJJlpOB. R= abc 4S l(eBTJl em1caHHOH OKpyll(}lOCTM - TOLfKa nepecetJeHl.UI 6HCCeK1'pHC. 2S r=--- a+b+c HeK0Topb1e csoH.crna Me,[(11a11, 611cceKTp11c 11 BblCOT Meoua11bl nepeceKwomCJt 6 00/IOU mo~Ke u mo~KOU nepece~eliW! OeJU1mc11 6 om11owe11uu 2 : I. c~uma11 om 6epwu11bl. h~C ~a Ilpl!MoyrOJJbHblH 'IpeyrOJlbHl1K c TeopeMa Iillljlaropa. c2 = a2+ b2 S= ab 2 ,lJ,n11tta OKpy)l(HOCTH C = 2nR, IlJJOl..llaJlb Kpyra S = nR. 2 R nR. 2 • CV IlnoIU3Jlb Kpyrosoro ceKTopa no l s = -36_0_0 · nnR • b c--:. f"i:""':. MHHa t1yrH l =--0-. n h=!!__=~acbc; a=vacc; b=vbcc 0 180 c ti (n - 2paoyCHaJ1 .Mepa •feHmpanbHOZO yZ11a) . b a IlnOIU3Jlh Kpyrosoro cerMett 2 Ta sm a=-;;; cosa=c b @ rrR o 1 R2 . o S =--·n ± - sm n a b 36if 2 ctg a= b; tg a=~ R 3HaK «+» Haoo 6pamb, Ko2oa ECJ1u ~ =30°, mo c =2a. Q n° 180° < n° < 360°, a 31/aK «-» llQOO PaJ1ttyC snHCaHHOH oKpy)l(Hocrn: ab a+b-c r r a+b+c 2 c PaJ111yc om1caHHOH OKp)l)KHOCTM R = - 2 I . Dpo113soJJbHhii1 4eTb1pexyronbtt11K ~qeTblpexyroJlbHHK, o nHcaHHblH OKOJIO OKpy ll(}lOCTH {Js h dd r=- = - ' - 2; 2 4a s a +c= b + d a+b+ c+ d 2 S = aha = bhb S = ab sin a ·r d 2 + d 2 - 2(a2 +b2 )I 2- S d1d2sin rp 2 S = d1d2 2 S = ah. = 2ar = a 2 sin a. 4. IlpllMOyrOJJbHl1K S = ab = d 2sin rp 2 5. Tpanel(HJI (h - 6blCOma, di. d2- oua20Ha.w) EF= a+b . S= d1d2 sinrp 2 . 2 a-b S= - - ·h = EF ·h..., 6pamb, K0200 0°< n ° < 180°, ( n° - zpaoyc11aJ1 A1epa i;e11mpanbHOZO yZ11a) HeKOTOp&1e ceoiiCTBa en11catt111>1x yTJJoe: I . Bnuca1111blu y20J1 pa«e11 no!IOBUHe J.feHmpa!lb· HOzo y2J1a, onupG/ouiezoc11 11a my :J/Ce oyzy; (6nllCGllllblU y20J1 pa8e/I nO!I06U/le oyzu, 110 Komopy10 OH onupaemc11). a=~=_!_! 2 2 2. BnucaH1tble Y2llb1, onupa10uiueCJ1. Ha ooHy u my :J1Ce oyzy, pa6/lbl. 3. Bnuca1111ble Y2llbl, onupa10uiueCJ1. 11a oua.Memp, npR.Mbte CooT11ouieHl1ll: Me)l()zy ,[(Jll1HaM11 xopA, OTPe3KOB KacaTeJJbHhIX 11 ceKyIUHX I. ab = cd 2. AB =AC ~ An4. AD-AE = AB-AC £J §)A D A ilnOIUllJlb, PllJIHYCbl BIIHCaHHOH 11 01111caHHOH OKPY)l(HOCTeH (a - cmopo1w, r - paouyc snuca1111ou 0Kpy:J1C11ocmu, R- paouyc onuca1111ou oKpY:JICHOcmu). r R s a a a 2/J lpeyrOJJbHHK 2,./3 J3 -- 4 a a a2KBllJIPaT - Ii2 a/3 a 3a 2 /3wecmyro.nhHHK -- --- 2 2 a a a2 n fl · )T0.1b HHX ..., 180°1 ..., . 180° 1 0° _tg- - ~sm -- 4 tg-~ n n n
  • 33.
    HQ nJIOCKOcmu l. PaccTOsim1eMe)!(L()' ToqKaMH A(x1; y 1) 11 B(x2;Y2) _ f( _ )2 ( _ )2AB - v X2 X1 + Y2 Y1 2. Koop,1111HaTbI (x; y) cepe,11HHbI OTpe3Ka c KOHllaMH A(x1;Yi) 11 B(x2; Y2) X1 +X2 y = Y1 +Y2 x=-2- , 2 3. 06ll.lee ypaimett11e npsiMoi1, nepnettn11Ky- 11sipttoH. BeKTOpy n(a;b) ax+ by+ c = 0 4. Ypasttett11e 0Kpy:>ICHocn1 c pa,1111ycoM R 11 c 1..1ettTPOM s rnqKe (xo; Yo) (x-xo)2 +(y-yo)2 = Ri 5. EcJJH A(x1;y1) 11 B(x2;y2), TO Koop,1111ttaTbJ BeKTOpa: - ( ) AB X2 -x1:Y2 - Y1 MO.llYJlb BeKTOpa: iAsi=~~(x-2--x-1)2-+-(Y_2___Y1-)2 6. CJJO)l(ett11e seKTopos a(a1;a2)+b(b1;bi}=c(a1 +b1;a2 +bi} 7. YMHO)l(ett11e seKTopa(~) Ha 'IHCJJoA (a1; a2 ) A= (Aa1; Aa2) 8. CKanS!pttoe npOH3Be,!leHJ1e BeKTOpOB aMb ; ·b = l;l·lbl·cosq;, f,!le (/) - yroJJ Me)l(,!ly BeKTOpaMH QM lJ 9. CKaJJsipttoe npoH3se,11ett11e seKTopos a(al; G2) H b(b1;b2) a·b = a1b1+a2b2 I0. Koc1myc yrna Me)l(,!ly seKrnpaMH a(al; G2) H b(b1; b2) a·b a1b1+a2b2 cos <p =-=-=- =-----,,= ====----;===== lal·lbl ~a12 + a; .~b12 +b; 11. Heo6xo,1111Moe 11 nocTaTO'IHoe ycJJos11e nepneH.llHKYllS!pHOCTH BeKTOpOB ;(a1;aJ 11 b(b1;b2) a·b=0 MilM a1b1 +a2b2 =0 W (R paouyc oc1106m11<11 11wm11opa) 2 s 6oK= 2rrRH; v= rr.R H ; s nonH= 2rr.R(R + H) (R - paouyc OCH06G/IUJI KOuyca. - o6pG3ylOU(aJI KOH)'CG) 1 2 s 60K = TTRZ; v =3TTR H ; SllORH = rr.R(R +1) (R1 u R2 paiJuycw ocH06aH111i KoHyca, I 06pG3y1011JGJ1 KOHyca) S""'" =1t(R1 +RJI - -.r(R1 2 + R~) I~ BnpocmpaHcmBe l. PaccTOSIHHe Me)!{,11y TOqKaMH A(x1; y 1; z1) 11 B(x2; Y2; z2) - ------------- AB= ~(x2 -x1)2 +(Y2 -y1) 2 +(z2 -z1)2 2. Koop,1111ttaThl (x; y; z) cepe,11HllliI OTPe3Ka c KOHUaMH A(x1;y 1;z1) H B(x2; Y2; z2) X1 + X2 y = Y1 + Y2 z = Z1 + Z2 x=-2-, 2 2 3. 06mee ypasttett11e nJJOCKOCTH, nepnettn11- KyJ1S1pHoH BeKTOpy n(a;b; C) ax + by + cz + d = 0 4. YpasHeHHe c¢epb1 c pa,1111ycoM R 11 c 1..1eHTPOM B TO'IKe (xo; Yo; zo) (x-x0)2 +(y-y0 )2 +(z-z0)2 = R2 5. EcJJH A(x1; Y1; z1) H B(x2; Y2; z2), TO KOOp,!IHHaTbl BeKTOpa AB(x2 -x1;y2 -y1;z2 -z1) MO,!lyJlb BeKTopa IABI =~-(x-2---X1_)2_+_(_Y2___Y_1)-2-+-(z-2---z1-)2 6. C11o)!{eHHe seKTopos ;(a1;a2;a3)+ +b(b1;b2;b3)= ~(a1+b1; a2+b2; a3+b3) 7. YMHO)l(eHHe BeKTopa (~1;a2;G3)Ha '111CJJO , (a1; a2; a3) ,= (J.a1;Aa2; Aa3) 8. CKansipttoe npOH3Be,!leHHe BeKTopOB aH b ; .b= 1;1·lbl. cos(/), r,11e cp - yron Me)l(,!ly seKTopaMH a Mb 9. CKMJ1pttoe npo113se,11ett11e seKTOpos ;(a1;a2;a3 ) 11 b(b1;b2;bJ a·b = a1b1+a2b2+a3b3 I0. Koc11ttyc yrna Me)l(,!ly seKTopaMH ;(a1;a2;a3 ) H b(b1;b2;b3 ) a.b a1b1 + a2b2 + a3b3 cos (/) =-=-=- =---;:=:::i::::::===----"-o=="====- lal·lbl ~a12 +a;+a; ·~b12 +bi+bi 11. Heo6xo,1111Moe 11 ,11ocTaTO'llloe ycJJos11e nepneH,!IHKYJJS!pHOCTH BeKTOpOB ;(a1;a2;a3) 11 b(b1;b2;bJ Sc</Jepbl = 4n.R2; Vmapa= ~ 7T. R3 4acrn wapa 1. lllapoeoil cer MeHT (h 6blcoma ceZA1e11ma) 9, V=nh'(R-H s 60K = 2rr.Rh 2. lllapoeoil ceKTop (h - B1>1coma cezwe11ma) ~ s llOlH = nR(2h+~2Rh-h2 } ~ V =3._rr.R2 h 3 3. lllapoBOH C.lOH (h Bblcoma CIOR} I : 1 : : V= - ith + - ;r 'i + r- h: 6 2 - s = _ ;rRh 0603Ha'leHHS!: H Bbtcomo, S00• - ruioz1.1oob 60K0601/ n0Bepx11ocmu, S""''" - tUIOllfOOb noJ111oii no6epx11ocmu, V - o6oi!M. (Soc,,- fl.llOUJGOb 0C/106GHUJI, p - nepUMemp OCH08G/lllJ1) I. 2. 3. HaKJIOHHaJI npli3Ma (I - 6oK060e pe6po, Pce4 - nep1wemp nepne11ouKyJ111p110- 20 ce4e11u11, Sce4 fl.llOllJGOb nepne110UK)1J1Jlp11020 ce4e111<11) S OOK = Pc••l; V = See.I = Soc11H; SnOAH= S6oK + 2 SoCH IlpllMaJI np113Ma Riff Ljj S6oK= Poc11 H; V = Soc11 H; snORH= S6oK + 2SOC/I IlpllMOyronbHhIH napa!lnenemme,[l (a, b, c - ezo U3.Mepe11W1, d - OU02011Q/lb) d 2= a2+b 2+c2; V =abc; Sno.•11 = 2(ab + be + ac) 4. Ky6 (o - pe6po) a@ d = a,./3; V = a3 ; (I - ano</JeMa) 2. IlpaBHilhHall ID!paMH,[la I - nepu.1i1emp oc1106011W1} S =.J:._P·l60K 2 3. IlpOHJBOJihHaJI yceqeHHaJI mtpaMH,[la ~ (S, u S2 - nllOUJao11 oc1106011uii) C1? Sno,,,, =S60K+S,+S2; v= }__ H. (s1+s2+~s1si}3 4. IlpaBHilbHaJI yceqeHHaJI nHpaMH,[la (P1u Pi - nepuMempbt oc1106011u1i) l!!s>S'"' =~(P,+P,) I 11HqlopMilljHOHHO-Cnpaao4HaR ra6n"1jil C OOO '1H<Ponnacr-. 2004 r. Mocl<Sa. KaJJMpCKoe wocce. 21 E-mat ~"' ... iJIOOfast. llJ 0
  • 34.
    PaanM'IHb1e BMAbl yrnoa A 0 Aeayrna Ha3b1Ba10TCH cMe)f(HblMl1, ecn11 y H111X OAHa CTOPOHa 06LI.1a5!, a Apyr111e CTOPOHbl 51Bn51- IOTC51 AOnOJlHl1TellbHblMl1 ny'laMl1. LAOB 111 LAOC- CMe)f(Hble yrllbl. • CYMMa CMe)f(HblX yrnoe pasHa 180° A B 0 c D Aea yrna Ha3b1Ba10TCH sepTMK311bHblMM, ecn111 CTOPOHbl OAHOro yrna 51Bfl5llOTC51 AOnOllH11Tellb- HblMl1 11y'laM111 cTopoH APYroro yrna. LAOB 11 LDOC eepT111KallbHbl8, LAOD 111 L.BOC eepT111KallbHble. • eepT11KanbH01e yrnb1pasHbl (LAOB = LDOC; LAOD = LBOC). a A B I 1 /2I b I D C 1 I np51Ma51 AC Ha3b1saeTcH ceKy1qeii no oTHowe- H11110 KnpHMblM AB 11 CD, ec11111 oHa nepeceKaeT o6e npHMb1e. Ecn11 np51Ma51AC51BnReTC51 ceKy- LI.1911 no OTHoweH11110 K np51Mb1MAB, CD 111, Kpo- Me Toro, TO'IK111 B 11 DJ19)f(aT BOAHOJil nonynno- CKOCT111 OT ceKyLI.1el1 AC, TOyrnbl BAC 111 DCA Ha3b1BalOTCR BHYTP8HHMMM OAHOCTOPOHHMMM. a B A D Ecn11 AC- ceKyUaR no OTHOWeH1110 AB 11 CD, a TO'IKl1 B 111 D ne)f(aT s pa3Hb1X no11ynnocKo- cT5IX OT AC, To yr11b1BAC11 DCA Ha3blBalOTC51 BHyTpeHHMMM HaKpecr nelK31qMMM. a " 3 1 b Coo1se1c1seHHbtMM Ha3b1BalOTC51 yrnb1npR- MblX a, b c ceKyLI.1el1. Yrllbl 1 111 3 - COOTBeTCTB8HHble. 06PA30BAHME YacTb 2 ~ noc1poeHHe rpMryp AeneHMe otpe3Ka nononaM . c. A 0 ; c, nocrpoeHMe. 1113 TO'leK A 11 B l.lli1PKY119M on111cb1saeTcsi oKpy)f(- HOCTb pa,o,111ycoM AB. nycTb c11 C, - TO'IK111 nepece'l9Hl151 3Tl1X OKpy)f(HOCTel1. 0Hl1 ne>KaT B pa3HblX nonynnOCKOCTRX OTHOC111T91lbHO np51MOJil AB. COOMOUblO 11111H9JilKl1 C08A111Hl1Tb TO'lK111 C 111 C,. 0Tpe30K CC, nepeceKaeT oTpe3oK AB a TO'!Ke 0. 3Ta TO'lKa - C9P9Al1Ha 0Tpe3Ka AB. npoB8A8HH8 nepneHAHKynRpa KAaHHOH np!IMOH '-lepe3 TOYKY 0 npoeecT11 np51MYIO, nepneHA111KYl151PHYIO ,QaH- HOJil np51MOl1 a. PeweHMe. Bo3MO>t<Hbl ,o,sa cny'la51: 1) TO'lKa 0 119>Kl1T Ha np51MOl1 a; 2) TOYKa 0 He 118>K111T Ha npSlMOJil a. Cny'laif 1 . ..c B 0 a nocTpoeHMe. 0Tfl0)f(l1M OT TOYK111 0 no pa3Hble CTOPOHbl OT Hee Ha np51MOJil a o,o,111Hai<o0b1e oTpe3Kl1 OA, OB. npoeeAeM ,o,ee OKPY>KHOCT111 OA111HaKoeoro pa,o,11yca A.Bc l.l9HTPOM a TO'l- Kax A 11 B cooTBeTCTBeHHO. OH111 nepeceKaioTcsi a TO'lKe C. npoee,o,eM npsiMyl-0 (QC). 0Ha nepneH,0,11KY!151pHa np51MOl1 a. 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B noc1poeHMe. 1113 eepW1'1Hbl O,o,aHHoro yrna, KaK 1113 4eHrpa, on11weM OKPY>KHOCTb np01113BOllbHOro pa,o,111yca. nycTb B 11 c - TOYK111 nepeceYeH11si ee co cTopoHaM1'1 yrna. nocTpo11M eUe ,o,ee OKPY>KHOCT11 c reM >Ke pa,o,11ycoM c l8HTpaM11 a B 1-1 C. nycTb D- TOYKa 11X nepeceYeHl151. Tor,o,a [AD) - 11CKOMaR 6111cceKTp111ca yrna A. nposeaeHMe np1Moit, napannenbHOM aaHHOH Yepe3 3a,QaHHYIO TOYKY A npoeecT11 npsiMylO, napannenbHYIO AaHHOl1 np51MOJil a. D .rA ... ' a I I I · B c nocTpoeHMe. '-lepe3 33,QaHHYIO TO'IKYA 11 npo113BOllbHYIO TOY- KY B npHMOJil a npose,o,eM npsiMy10 AB. nycTb C - npo113- BOl1bHa51, OTl1111'1Ha51 OTB TO'IKa np5lMOl1 a. nocTp01'1M OTnyya AB B nonynnocKOCTb, He co,o,ep>KaUYIO TOYKY C, yron, pas- Hb11il yrny (ABC). nycTb [AD) - CTdpOHa nocTpOeHHOrO yrna. Tor,o,a np51MaA AD II a. 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  • 35.
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Asa- np11MoyronbHb11 tpeyronbilHKa ffOA06Hbt. ecnM: 1) uxK-a:rer1J1.nponapl.f~HMbH_bJ; ~=----------~ 2) KarerHr11n_ore1;1y3a opHo.ro rpeyFotTbf!JtKa njJo- nopl.f"lfOHaJlbHb.l ~aJ.BT.JI J.1 PY.flOT8H¥38J[py.rexi'.o; .3j' lfBa yrna O!JHOro rpeyronbH/l!*a11affffbl 1J8YM.yrnaM 11pyrora~ . ' HH<t>opMal.IHOHHO- cnpaeo'iHaff Ta611HL1a © 0 00 «V1Hcpon11acr", 2006 no;o,nHC8Htj a ne•aTb 28. 12.os. r..pa)I( 40003K3. 3ali'.a3 t-P 3106. "13,qarenb 000 •fl1H¢onnacr», Moci<ea, Kaw'1pcKoe wocce, 21. r..notpa</>MR ooo.s..sa-Crap•, 107023, MocKsa, yn. 311eKTposa1JOp.CK8A, 20 -
  • 36.
    3nnMnCOM Ha3blBaeTC!I reOM0TPl1'l0CK00M0CTO TO'l0K, CYMMa paCCTO!IHl111 OT KOTOPblX AO ABYX 3aAaHHblX TO'l0K F, 11 F;, Ha3b1saeMb1x itioKYC3MM 3nn11nca, ecrb sen11'111- Ha OOCTO!IHHaR. 2 2 YpaaHeHMe 3nnMnca: x2 + y2 = I . (I b 3A0Cb HaYano KOOPAl1Har !IBn!leTc!I 4eHTPOM c11MMerp1111 31111110Ca, a OCl1 KOOPAl1HaT - ero OC!IMl1 Cl1MM0Tpl111. np11 a >b ¢0Kycb1 3111111nca neJKaT Ha oc11 OX, np11 a <b ¢oKyCbl 3111111nca neJKaT Ha oc11 0 Y. a np11 a = b3nn11nc craHos11rc11 oKpYJKHOCTblO (¢0Kycb1 3nn11nca B3TOM CJlyYae COBOaAalOT c 4eHTpOM OKPYJKHOCT11). TaKl1M o6- pa30M, oKpy)l(HOCTb ecrb '18CTHbti1 cny'lai1 3nn11nca. Orpe30K F.Fi = 2c, rAe c = ~la2 -b2 I ,Ha3b1eaerc11 itio- KYCHblM paccro11HMeM. To'iK11 A, B, C 11 DHa3b1Ba10TC!I aepwMHaMM 3nnMnca. Orpe30K AB = 2a Ha3b1eaerc11 6onbwoii OCblO 3nnMnca, a orpe30K CD = 2b - Manoii , ,2 YpaaHeHMe rMnep6onbl MMeeT BMA: 4-~ = I . a b 3TO ypaBH0Hl1e Ha3b1Baerc!I KaHOHl1'i9CKl1M ypaBH0Hl19M r1o1nep6onbl. Caoiicrao. r11nep6ona He "1Meer 061J.111X TO'l0K c OCblO Oy, a OCb Ox nepeceKaer s ABYX TO'IKax A(-a; 0) 11 B(a; 0), KOTOPblB Ha3bl83IOTC!I eepWMH3MM r 11nep60llbl. Orpe30K AB Ha3b1eaeTC!I AeiicTBMTenbHOii ocbio r11nep- 6onb1, ero An11Ha paeHa 2a. 'i11c110 a Ha3b1Baerc!I Aeiicr- BMr enbHOii nonyocblO r11nep6011b1, Yli!CllO b - MHMMOii no- nyocblO. CeoiiCTBO. r1i1nep6ona 11M00T ABB B3al1MHO nepneH,!111KY- Jl!IPHble OCl1 Cl1MM0Tpl111. <1>11rypa, Ka)KAa!I TOYKa KOTOpol:l pasHoy,11a11eHa OT AaHHOlii TOYK11 A 1i1 ,11aHHOlii npsiMolii I HaJb1saeTcS1 napa6011olii. y 2 = 2px 3ro ypaBH0Hl1e H33bl830TC!I KaHOHl1'i0CK"1M ypaeHeHl10M napa6011b1. 06PA30BAHME 3nnMnc c OCblO 3nnMnca. 'il1CJ10 6 =a' E < I Ha3blBaeTC!I 3KC"eH- TpMCMT0TOM 3nnMnca. F,M =a+tx, F,M =a-ex Caoiicrao. CyMMa paccroS1H11i1 or n106ol1 TO'iKl1 3nn11nca AO ero ¢oKyCOB eCTb een11Y11Ha nOCTO!IHHa!I 11 paeHa!I YABOBHHOlii 6011bwel1 no11yoc11. F,M+F,M = a+sx+a- sx =2a Caoiicrao. 311n1,1nc 11Meer ABB s3a11MHO nepneHAl1Ky1111p- Hb1e OCl1 CIAMMeTplAl1. Caoiicrao. 3nn11nc "1Meer 4eHrp c11MMerp1111. LjeHTp Cl1MM0TPl111 3J1Jlli!nca Ha3blBaeTC!I "eHTPOM 3n- nMnca. np!!Ma!I X = -d Ha3blBaeTC!I AlilP0KTp"1COl1, COOTBBTCTBY- IOlJ.1011 ¢oKycy F,(-c; 0) rAe d = ·~ > a . Hap!IAY c 3TOlii A11P0KTP"1COl1 BBOA!IT np!IMYIO x = d, KOTOpa!I !IBJ1!10TC!I rMnep6ona Mee CBOMCTBa CaoiiCTBO. r11nep6011a 11M00T 40HTP Cli!MMeTp1111. LjeHTP Cl1MM9TPl11i1 r11nep60Jlbl Ha3bl83IOT 40HTPOM ntnep- 6onbl. Caoiicm o. r11nep6011a nepeceKaerc!I c np!IMOl1 y =kx nplA lkl< gBABYX TO'IKax. Ecn11 1"1~ i TO 061J.111X TO- 'leK y npsiMolii 11 r11nep6onb1 Her. To'iKl1 F, (-c; 0) 11 F1 (c; 0) Ha3b1sat0TCS1 itioKycaMM rM- nep6onb1. 3,11ecb c= Ja2 +b2 • 'ieM M0HbW0 3KC4eHTPl1Cl1T0T, T0M 6onee r11nep6011a ClKaTa KOCl1 Ox. n 6 ~apa ona Mee CBOMCtBa CaoiiCTBO. napa6011a pacnonoJKeHa B nonynnOCKO- CTlil X :i: 0. TO'IKY (~, o) Ha3b1Ba!OT ltJOKYCOM napa6onbl 11 0603Ha- YalOT 6yKsolii F n p - P!IMa!I x = -2 8 KaHOHl1'leCKOlil Cll1CT0Me KOOp,1111HaT CaoiiCTBO. napa6ona "1M00T OCb C11MM0TPl11i1. Ha3b1Ba8TC!I AMP0KTPMCOii napa6onbl. PaccTO!IH110 OT Hee Ocb Cl1MMeTp1111 HaJbieaerc!I ocbio napa6onb1. TOYKa ne- AO¢ oKyca Ha3b1saercS1 itioKanbHblM napaMeTpoM napa60- peceYeH1111 napa60llbl c OCblO H33blB38TC!I aepwMHOii na- Jlbl. 0'leBl1AHO, OH paeeH p. 3Kc4eHTP"1Cl1T0T napa60flbl no pa6onbl. Bepw11Ha napa60Jlbl BKaHOHl1'i0CKOlii Cl1CT0Me onpBABJlBHlillO no11arat0T paBHblM BAl1H114e, TO eCTb e=1. KOOPAl1Har HaXOAMTC!I e HaYane KOOpA11HaT. Tenepb csoliicrso, 'lepe3 KOTopoe Mbl onpe.11en11n11 napa- '°iaCTb 3 A11P0KTPlilCOlii, COOTB0TCTBYIOIJ.l0McPOKycy Fi(c; 0). nyCTb M (x,, y,) - TOYKa 3J1Jll10Ca, TOfAa ypaBH0HM0 Ka- carenbHOii K3MMncy B AaHHOM TO'IK0 11MeeT 811A'. x,x + YtY =I a 2 bi . YcnoaMe KacaHMA np11Moii y = mx+k , xi y· . 1i1 3nnMnca 2 + 2 =I . a b k2 = 1n2a 2 +/fl. y bD M A Fi d -a -c 0 c -b c B a d X 0603Ha'ili!M d = ~ ' TO, OOCKOllbKY AJl!I r11nep60llbl e >1, li!M88M d <a. np!!Ma!I x =d Ha3blB38TC!I AMP0KTPMCOii r11nep60nbl, COOTBBTCTBYIOUIBlii cfJOKyCy fj. np!IMYIO X = - d Ha3blB3IOT AIAPBKTPl1COlii, COOTBBTCTBYIOUIBlii ¢oKycy F,. 811,11 r11nep6011b1 11 ee ,1111peKrp11c s KaHoH11YeCKOlii c11cre- Me Koop,1111HaTnp1i1ee,11eH Ha p11c. y -c -d d c x 6ony, s HOBblX TepM1i1Hax MOlKHO ccpopMyn11poearb cne- .llYIOIJ.ll1M o6pa30M: lll06a!I TO'!Ka napa60llbl paBHOYAane- Ha OT ee cpoKyca Iii AIApeKTpl1Cbl. B11A napa6011b1 a KaHoH11YecKolii c11creMe KoopA11Har 11 pacno110JKeH11e ee A11peKrp11cb1 np11seAeHbl Ha p11c. y M -p/2 I~ x -
  • 37.
    • ' nonstpHaSI CMCTeMa KOOPAHHaTcraBllT BCOOTBeTCTBMe KID!(J011 TO'lKe Ha OJlOCKOCTM napy 'll1Ce11 (p; <p). 0CHOBHblMl1 OOHSIT11SIMH 3TOM Cl1CTeMbl SIBJlSllOTCSI TO'iKa OTC'leTa - nonioc - 11 ny'i, Ha'l11Hat01J.11111CSI B3TOH TO'iKe, - nonstpHaSI OCb. KOOPAMHaTa p - paCCTOSIHl1e OT TO'iKM.110 nonioca, KOOPA11Hara <p - yron Me)l(AY nonsipttol1 OCblO 11 orpe3KOM, coe.a11HS1t0- l1MM nont0c 11 paccMarp11saeMyio TO'iKY, KOropb1i16epercsi co 3HaKoM «+», ecn111 yro11 or oc11 AO orpe3Ka Bb1'111c11S1ercS1 npor11s 'lacosoi.1 crpenK11, 11 co 3HaKoM «-» s npor11sono- no)l(HOM cny'iae. Ba)l(HO noH11MaTb, 'iTO Y11cno <p Bnonsipttoi.1 c11creMe onpe.aeneHOHe OA- H03Ha'lHO: napaM 'i11cen (p; cp +2nn) coorsercr syer OAHa 11 ra)Ke TO'lKa np11 n106b1x Ha- rypanbHblX n. .Qnsi nont0ca p = 0, ayron cp He onpe.aeneH. 150° 180° 210° 120° goo .. 240° 270° 60° ..........__(p .... 300° nonRpHafl CHCTeMa KOOP,QHH8T. 30° 330° nonS!pHble KOOPA11HaTbl nerKO npeo6pa30BaTbB,fleKapTOBbl. nycTb (~; y) - KOOPAl1HaTbl TO'lKl1 BJl0Kaproaol1 Cl1CTeMe KOOPA11HaT, (p; cp) - BnonS!pHOl1. Tor.Qa { x =pc~scp, y = pstncp. <l>opMynb1o6parHoro nepexo.aa: p = Jx2 +y2, <p = arctg ~, x ;t: 0, 1t m=- x= O y> OT 2 ' ' ' 1t tn = - - x= O y< OT 2 ' ' . QMnMHAPH'leCKaA Hcc1JepM'leCK3A CHCTeMbrKOOPAHH3T~ - , . ~ Ha p11cyHKe noKa3aHbl 411n11HAPl1'iecK11e p, <p, z 111 c¢ep111YeCK111e Koop.Q111Harb1 r, fl, <p (nonsipHb1i:1 pa.a11yc, w11pora 11 .Qonrora). z z ......._ .._ .._ '-............ M., (} r 0 y I / cp p : /// y . I / - - --·-- - -- --_../ M' p=.Jx1+y2 , x=pcoscp tg<p = ~ , y = psihcp z =z z cos<p= / , y=rSin0coscp "IJX2+y2+z2 ta1n = Y z = rcos0e ·'t' ~t , AeyrpaHHblHyron - 3TO 'iaCTb npocrpaH- a crsa, 3aKnt0YeHHaS1 Me)l(JlY ABYMRnony- B nnocKocrstM11, 11Met01J.1111M11 OAHY061J.1YIO A ...-------(3;.. rpaH11uy. nonynnocKocr111 o. 11 ~. o6pa3Yt01.ll11e .asyrpaHHbli.1 yron, Ha3b1sat0rcS1 ero rpaH11- MM. 06U,aSI npsiMafl 3Tl!1XrpaHei1 Ha3blBaeTCR pe6pOM AByrpaHHOfO yrna. nycTb TO'iK11 A11 B B3RTbl Ha pe.6pe AByrpaHHoro yrna. .QsyrpaHHbli'.1 yron o6o3HaYaercl! ABYMSI 6yKBaM111 yron AB. TpexrpaHHblH yron OnpeAeneHMe: TpexrpaHHbli'i yron - aro YaCTb npocrpaHcrsa, orpaH11YeHHast rpe- MR nnocK11M11 yrnaM11 c o6u.iei:1 sepw11- HOl1 11 nonapHo 061J.111M11 cropoHaM11, He ne>Kallll1Mlll B0.QHOH nnOCKOCTl1. 061J.1aS1 sepw11Ha 0 3r11x yrnos Ha3b1saercsi eep- WMHOi'i rpexrpaHHoro yrna. CropoHbl yr- c a nos Ha3b1saiorcsi pe6paMM, nnocK11e yrnb1 np11 sepw11HerpexrpaHHoro yrna Ha- 3b1Baiorcsi ero rpaHAMM. rpaH11 rpexrpaHHoro yrna 06pa3yior AByrpaHHbJe yrnb1. TeopeMa «HepaeeHcreo rpeyronbHMKa AJlA rpexrpaHHoro yrna»: Ka>K.Qb1l1 nno- CK11!1 yron rpexrpaHHoro yrna MeHbwe cyMMbl .asyx Jlpyr111x ero nnocK11x yrnos. TeopeMa: a + y + ~ <360°. .QpyrlllMlll CJlOBaMl1, CYMMa nnOCKlllX yrnO,BrpexrpaHHOfO yrna MeHbWe 360°. TeopeMa "TeopeMa KOCMHycoe AJlA rpexrpaHHoro yrna»: cosa= cos 13 cosy + sin 13 siny cos A , fA9 a, f3,y - nnocK11e yrnbl, A - ABYri}aH- Hbllli yron, cocrasneHHbli1 nnocKOCT5lMl1 yrnos f3 11 y. 3aMe'l3HMe. cnoMOUblO A0Ka3aHHOi1 reopeMbl MQ)!(HOBbl'll1Clll1Tb aenl1'il1HY .asyrpaHHoro yrna, 3HaH nnocK111e yrnbl rpexrpaHHOro yrna: A - cos(x - cosf3cosy cos - . (.l • sin ..,siny Ecn111 rpaH11 n11ocK11x yrnos s3a11tMHO nepneHA11KynstpHbl, nony'laeM cpopMyny rpex KOC11Hycos: cos a= cos~ cosy TeopeMa «TeopeMa CMHycoe AflA rpexrpaHHoro yrna»: sina sin f3 srny Cnpase.Qn11so paseHcrso . A = . B - . C Slll SID SH'l fAe a, ~. y - nnocK111e yrnb1 rpexrpaHHoro yrna; A. B, C- npor11so11e)l(au.i11e 11M AByrpaHHb1e yrnb1. OnpeAeneHMe: HecKOnbKO.nnocK11x yrnos c 061.lll1M Ha'i~noM 0, 113 KOTOPblXH11- KaK11e ABa He ne>KaT BOJlHOti nnOCKOCTl1, o6pa3ylOTMHOrorpaHHbli'i yron. 3Tlll nnocK111e yrnbl np11 aepw11He MHOrorpaHHoro yrna Ha3b1saiorcsi rpaHAMM, acropo- Hbl 3r11x yrnos - pe6paMM, roYKa 0 - eepwMHOi'i MHororpaHHoro yrna. no ~11c11y rpaHei:1 MHororpaHHblHyron Ha3b1saerc51 rpexrpaHHblM, YeTb1pexrpaHHblM111 T.Jl. Ecn11 see rpaHIA MHOfOfi}aHHOfO yr11a HaXOJlSITCSI c O.QHOl1 CTOPOHbl OT Ka>KAOlli 1113 nnOCKOCTei.1 ero rpaHei:1, yron Ha3blBaeTCSI BblOYKJlblM. TeopeMa: Ka>t<Jlbli1 n11ocK11i1 yron MHororpaHHoro yrna MeHbwe cyMMbl scex oc- ranbHblXero nnocK11X yrnos. TeopeMa: CyMMa nnocK11x yrnos Bb1nyKnoro MHororpaHHOro yrna MeHbWe 360°. li1H<J>OpMa41<10HHO-CnpaeoYHaS1 Ta6ni.14a © 000 "111Hcj:Jonnacr•., 2006 r. MocKsa, Kaw"'pcKoe wocce, 21 E- mail: mail@infoplast.ru, http://www.infoplast.ru Ten.: (095) 320- 94-89/88 no.am1caHO 8 ne48Tb 28.'12.05. T11paJ1<4000 3K3. 3aKa3 N'1 3106. /13,aarenb 0 00• l1H,Ponnacr•, MOCKBa, Kaw11pCKOe wocce, 2 1. Tunorpa<JJMR 000 «81<ea-C1ap•, 107023, MOCKBa. y11. 311eK-1po3aeo,acKaR, 20 -
  • 38.
    napannenbHOCTb npAMOit MnnDCKOCTM OnpeAeJleHMe.npHMaH 11 nnDCKOCTb Ha3blBalOTCH napannenbHbfMM, ecn11 OHl1 He 11MelOT 06lJ111X TOYeK. Ecn11 npHMaH a napannenbHa nnocKo- crn a, TO n11wyT alla. TeopeMa. "npM3HaK napannenbHOCTM npAMOii MnnocKOCTM». Ecn11 npHMaH BHe nnocKocrn napan- nenbHa KaKOiii-Hl16YAb npHMOiii Ha nnocKOcrn, TO 3Ta npHMaH napan- nenbHa 11 caMoiii nnocKOcrn. TeopeMa. TeopeMa ocneAe. Ecn11 nnocKOClb f3 npoXDAl1l Yepe3 npHMYIO a, napannenbHYIO nnDCKO- fl a PMCYHDK 1. a - HBKOTOpaH nnoCKOCTb, I - HB ne>Ka- L11aH e JTOii nnocKocrn npHMaH, /, - npH- MaH e nnocKocrn a, napannenbHaH !. cm a, 11 nepeceKae1 3lY nnocKOClb no npHMDiii b, TO blla. OnpeAeneHMe. npHMYIO b 11HDrAa Ha3b!BalOT cneAOM nnoCKOCTM /3 Ha nnDCKOCrn a. napannenbHOCTb ABYX nnDCKOCTeit OnpeAeneHMe. Ase nnocKocrn Ha3bl- sa10lCH napannenbHbfMM, ecn11 0H11 He 11MelOT 06U111X TOYeK. TeopeMa. «npM3HaK napannenbHOCTM nnOCKOCTeii». Ecn11 ABe nepeceKa10lJ111ecH npHMble DAHOiii nnocKOCTl1 COOlBelCTBeHHO napannenbHbl ABYM npHMblM APYrDiii AoKa3aTeJ1bCTBO. nposeAeM s AaH- HOiii nnOCKOCTl1 p KaK11e-n1160 ASe ne- peceKalOlJ111eCH npHMble a 11 b. Lfepe3 TOYKY A nposeAeM napannenbHble 11M npHMble a, 11 b,. nnocKOClb P,, npo- XOAHlJ1aH Yepe3 npHMble a, 11 b,, na- pannenbHa nnocKocrn P. AonycrnM, YTO Yepe3 TOYKY A npoxo- nnocKOCTl1, TO 3111 nnocKocrn napan- A11l APYraH nnocKOClb P,, TO>Ke na- nenbHbl. pannenhHaH nnocKoc111 P. 01Me111M Ha Heiii KaKyl0-111160 TOYKY C, He ne- PMCyHOK 2. P, ~ P, - 11aHHb1e nnocKocrn; a, ~ a, - npHMblB e nnocKOcrn P,, nepece- Ka10L11~ecH BTOYKB A; b, ~ b, - COOTBBTCTBBHHO napa11nenbHblB ~M npHMblB BnnocKDcrn P,. TeopeMa. Ecn11 ABe napannenbHble nnocKocrn nepeceYeHbl TpeTbeiii, TO OHa OCTaBJlHel Ha 3Tl1X nnocKOCTHX napannenbHble cneAbl. TeopeMa. Lfepe3 TOYKY BHe AaHHOiii nnocKocrn MD>KHD nposecrn nnoc- KDCTb, napannenbHYIO AaHHOiii, 11 np11- TOM TOJlbKO DAHY. A~7 ~~b/ >Kal!1yl0 s nnocKocrn P,. nposeAeM nnOCKOClb a Yepe3 TOYKl1 A, c 11 Ka- KYI0-111160 TOYKY B nnOCKOCTl1 P. nnocKOClb a nepeceYeT nnocKocrn P, P, 11 P, no npHMblM b, a 11 c. npH- Mb1e a 11 c He nepeceKalOT npHMYIO b, laK KaK He nepeceKalOT nnocKOClb P. CneAOSaTenbHO, 0H11 napannenbHbl npHMOiii b. Ho s nnocKocrn a Yepe3 TOYKY A MO>KeT npOXOAl1Tb TOJlbKO OAHa npHMaH, napannenhHaH npH- Moiii b. nonyYeHo npornsopeY11e. TeopeMa. 01pe3Kl1 napannenbHblX npHMblX, orpaH11YeHHb1e ASYMH na- pannenbHblMl1 nnoCKOCTHMl1, paSHbl. TeopeMa. Asa yrna c cooTseTCTseHHO napannenbHblMl1 11 OA11HaKoso Hanpa- sneHHblMl1 CTOPOHaMl1 paSHbl 11 ne- >KaT BnapannenbHblX nnOCKOCTHX. OnpeAenett11e. npHMaH Ha3b1sae1cH nepneH- Ha3b!SaeTCH 0Tpe30K npHMOiii, nepneHA11KY- IJMKynRpHoft nnoCKOCTl1, ecn11 OHa nepneHAl1- nHpHoiii AaHHOiii nnoCKOCll1, KOTOpbliii COeA11- KynHpHa Jll060iii npHMOiii 113 3TOiii nnoCKOCTl1. TeopeMa. «npM3HaK nepneHAMKynApHOCTM npAMOii MnnocKOCTM». Ecn11 npHMaH nepneHA11KympHa Ka>KAOiii 113 ASYX nepeceKalOlJ111XCH npHMblX nnocKOCTl1, TO OHa nepneHA11KynHpHa 3TOiii nnOCKOCTl1. PMCyHOK 4. a a - npHMaH, nepnBHA~KynHpHaH npffMblM b ~ C, ne>Kalll~M BnnocKocrn P ~ npHMaff a npoxo11~T Yepe3 TOYKY A nepeceYeH~H npHMblX b ~ c nnoc- Kocrn P. TeopeMa. nnocKOCTb, nepneHA11KynHpHaH OA- Hoiii 113 ASYX napannenbHblX npHMblX, nepneH- Al1KynHpHa 11 APYrDiii. TeopeMa. Ase npHMble, nepneHA11KynHpHble OAHDiii nnoCKOCTl1, napannenbHbl Me)l(Ay co- 6oiii. TeopeMa. Ecn11 npHMaH nepneHA11KynHpHa OAHOiii 113 ASYX napannenbHblX nnoCKOCleiii, TO oHa nepneHAl1KynHpHa 11 APYrDiii. TeopeMa. Ase nnocKoc111, nepneHA11KynHp- Hble OAHOiii npHMOiii, napannenbHbl Me>KAY co6oiii. OnpeAeneHMe.nepneHIJMKynRpoM, nposeAeH- HblM 113 AaHHOiii TOYKl1 Ha AaHHYIO nnOCKOClb, HHeT AaHHYIO TOYKY c TOYKOiii nnOCKOCll1. TeopeMa. Ecn11 113 OAHOiii TOYKl1 SHe nnoCKO- CTl1 nposeAeHbl KHeiii nepneHA11KynHp 11 Ha- KnOHHble, TO: AJ111Ha nepneHAl1KynHpa MeHhwe AJ111Hbl nl06oiii HaKnOHHOiii; • HaKnOHHble c paSHblMl1 npoeKljl1HMl1 paSHbl; • 113 ASYX HaKnOHHblX 60J1bWYIO AJ111HY 11Meel Ta, y KOTOpoiii 6onbwe npoeKljl1H. TeopeMa. «O rpex nepneHAMKynApax... Ecn11 npHMaH, npoBeAeHHaH Ha nnocKOCTl1 Yepe3 OCHOSaH11e HaKnOHHOiii, nepneHA11KY- nHpHa ee npoeK111111, TO OHa nepneHA11KYnHP- Ha 11 caMoiii HaKnOHHOiii. nycTb AC- HaKnOHHaH npHMaH KnnocKo- cT11 P, BC- npoeKl111H npHMoiii AC Ha nnoc- KOCTb P, T.e. BCE P, npHMaH BC nepneHA11- KynHpHa npHMOiii /, ne>KalJ1eiii s 3TOiii nnOCKO- CTl1. Tpe6yeTCH AOKa3alb, YTO HaKnOHHaH AC TaK>Ke nepneHA11KynHpHa npHMoiii I. PMCyHOK 5. p TeopeMa (o6paTHaA). Ecn11 npHMaH Ha nnoc- Koc111 nepneHA11KynHpHa HaKJlOHHOiii, TO OHa nepneHA11KynHpHa 11 npoeKljl111 HaKnOHHOiii. nycTb /..L CA, IE P, Tpe6yeTCH AOKa3aTb, YTO / ..L CB, rAe CBE P 11 HBnHeTCH npoeK1111eiii npHMOiii CA Ha nnocKOCTb P. nepneHAMKynApHDCTb ABYX nnocKocreit OnpeAeneHMe. Jiae nepeceKalOU111ecH nnocKo- cr11 Ha3blBalOlCH nepneH/jMKYflflPHblMM, ecn11 lpelbH nnocKOClb, nepneHA11KynHpHaH npH- Moiii nepeceYeH11H a111x nnocKocreiii, nepece- Kae111X no nepneHA11KynHpHblM npHMblM. TeopeMa. «npM3HaK nepneHAMKynApHOCTM ABYX nnocKOCTeii». Ecn11 nnocKOCTb npoxDA11T Yepe3 npHMYIO, nepneHA11KYnHPHYIO APYrDiii nnocKoc111, TO 3111 nnocKOCll1 nepneHAl1KYl1HpHbl. PMCyHOK 6. a- npHMaff, nepneHA~KynHpHaff nnocKOcrn P; P, - nnocKOCTb, npoxOAfflllaff Yepe3 npHMYIO a; TeopeMa. Ecn11 nnocKOCTl1 a 11 f3 s3a11MHO nepneHA11KYl1HPHbl, 11 KnnOCKOCTl1 a npose- AeH nepneHA11KynHp, 11MelOlJ111iii 06U1YIO TOYKY c nnoCKOClblO /3, TO 3TOT nepneHA11KynHp ne- >Kl1T BnnoCKOCll1 /3. TeopeMa. nycTb nnocKocT11 a 11 f3 nepneHA11- KynHpHbl nnOCKOCTl1 y 11 nepeceKalOlCH no npHMOiii a, TOrAa a ..Ly. a A b c p P, b - npffMaH, no KOTOpoii nepeceKalOTCff nnoCKOCTH p Hp . noKaJaTb, YTO nnOCKOCTH PM P nepneHJ)~K}'JlffPHbl _J
  • 39.
    OnpeAeneHMe. 06~HM nepneHAHKynRpoM ABYXCKpe~HBa/O~HXCR npRMb/X Ha3blBa- eTeR oTpe3oK e KOHL1aM11 Ha arnx npRMblX, nepneH,Ql1KYl1RpHblH Ka)f(,!OH 113 arnx npR- MblX. TeopeMa. ,Qse eKpeU11Ba10Ul1ee11 np11Mb1e 11MelOT 06U11H nepneH,Ql1KYl1Rp, 11 npMTOM e,Q11HeTBeHHblH. JleMMa. ,Qse eKpeU11Bat0U11ee11 np11Mb1e 11e>KaT Bnapa1111e11bHblX n11oeKoeT11x. OnpeAeneHMe. YrnoM MeJKAY HaKnoHHofl H nnOCKOCTb/O Ha3blBaeTeR yra11 Me)f(,!ly Ha- K110HHOH 11 ee opTOraHanbHOH npoeKLjl1eH Ha n11oeKOeTb. TeopeMa 06 061QeM nepneHAMKym1pe ABYX CKpe1QHBa101QMXCA npAMblX 0 a Ha p11cyHKe 7 noKa3aHa HaK110HHa11 AB, OB = IlpaAB, LABO- yra11 Me)f(,!ly Ha- Kl10HHOH AB 11 n11oeKoeTbt0 a. Ee1111 np11- Ma11 napan11e11bHa n11oeKoern, TO yra11 Me- >KAY Hl1MM no onpe11e11eH11t0 pa- seH 0°. Ec1111 np11Ma11 nepneH,Ql1KY- 11RpHa n11oeKoern, TO yra11 Me)f(,!ly Hl1Ml1 paseH go0 . Ee1111 {3- yra11 Me)f(,!ly npRMOH 11 n11oeKOCTblO, TO 0°< f3 < go0 • npose,QeM S n11oeKoern a npo113so11bHY10 npRMYIO b Yepe3 TOYKY B TaK, YT0- 6bl ocj_ b. nym LABO = {3, LOBC = y, LABC = <p. PaeeMaTpl1BaR np11Moyra11bHb1e Tpeyra11bH11K11 ABO, OBC, ACB, 11MeeM OB BC BC cosl3 =AB , cosy= OB , coscp = AB · . BC OB BC 3aMernM, YTO. AB = AB . OB 111111 coscp =cos 13 ·cosy . Mbl no11yY111111 ljJopMyny rpex KOCMHYCOB. 06parnre BH11MaH11e Ha TO, YTO n11oeKoern yrnoB f3 11 y B3al1MHO nepneH,Ql1KYl1RPHbl. 3aMe'laHMe. noeKOl1bKY yrnbl <p, f3 My OCT- pb1e, 113 cpopMyl1bl Tpex Koe11Hyeos e11e11y- eT, YTO cosl3 > coscp 110° <13 <cp . TaK11M o6pa30M, yrnoM f3 Me)f(,!ly HaK110H- HOH Mee opTOraHanbHOH npoeKLjl1eH Ha n11oeKOeTb RBl1ReTCR Hal1MeHbW11H 113 yr- 1108, o6pa30BaHHblX HaKl10HHOH e npRMbl- MM n11oeKoern a. DapannenbHOCTb npAMblX OnpeAeneHMe. napa1111e11bHOe npoeKrnposaHMe, npM KOTOPOM npoeKrnpylOUMe npRMble nepneH,QMKy1111pHbl Kn11oeKoern npoeKLjMH, Ha3blBaeTeR oproroHanbHb/M npoeKTHPOBaHHeM. OnpeAeneHMe. ,Qse np11Mb1e BnpoeTpaHeTBe Ha3b1Bat0Te11 napannenbHblMH, ee11M OH1111e>KaTB0.QHOH n11oeKOeTM 11 He MMelOT 06U11XTOYeK. OnpeAeneHMe. npRMble, KOTOpble He MMelOT 06U11XTOYeK 11 He napan11e11bHbl, Ha3blBalOTeR CKpe~HBa/O~HMHCR . 3aMe'laHMe. CornaeHo onpe11e11eHMIO, .QBe napan11e11bHb1e npRMble 11e>KaT BOAHOiii n11oeKoern. nerKo 3aMernTb, YTO Yepe3 .QBe napan11e11bHb1e np11Mb1e MO>KHO nposee- rn TOl1bKO OAHYn11oeKOeTb. TeopeMa. n110Ua.Qb opTOraHa11bHoi1 npoeKL111M MHora- yra11bH11Ka Ha n11oeKOeTb pasHa npOM3Be,QeHMIO era nl10Ua.QM Ha KOeMHye yrna Me>KAY n11oeKOeTblO MHOra- yral1bHMKa Mn11oeKoeTbt0 npoeKLjMM: Sap= S coscp . MHororpaHHHKOM BTpexMepHOM npo- CTpaHCTBe H83blBaeTeR COSOKynHOCTb KOHeYHOro '111e11a n11oeKl1X MHoroyro11b- Hl1KOS TaK3R, 'ITO: • K3)f(,!1311 CTOPOHa 11t06oro 113 MHOro- yro11bHl1KOS eeTb O,QHospeMeHHO eTopo- Ha APYraro (HO TOl1bKO OAHOro), H33bl- saeMoro cMe>KHblM e nepeblM no 3TOM eTopoHe; TeopeMa. '-lepe3 TOYKY BHe ,QaHHOH npRMOHMO>KHO npo- seern npRMYIO, napan11e11bHYIO ,QaHHOH, Mnpl1TOM TOl1b- KO OAHY. OcHOBHble noHATMA TeopeMa. «npM3HaK cKpe111Meaio111MxcA npAMblX». Ee11M O.QHa M3 ABYXnpRMblX11e>KMT Bn11oeKoern, a 11pyra11 nepeeeKaeT 3TY n11oeKoeTb BTOYKe, He np11Ha,Q11e>Kalleiii nepsoiii npRMOH, TO am ABe npRMble eKpeUMBalOTeR. pan11e11bHblXn110CKOeTllX, Ha3blBaeTell npH3MaTOHAOM. npH3Ma, nHpaMHAa Hyce~eHHaR nHpaMH- Aa - 'laeTHble e11y'la11 np11aMaT011Aa. Bee 60KOSble rpaHl1 npM3M3TOl1,Qa 11811lllOTCll Tpeyro11bH11KaM11 111111 '1eTb1pexyra11bHMKa- M11, np11'leM 'leTb1pexyra11bHb1e rpaH11 - 3TO Tpanelj1111 111111 napan11e11orpaMMbl. • OT 11t06oro 113 MHorayrOl1bHl1KOB, eocTa- e1111t011111x MHOrorpaHHl1K, MOlKHO AOMrn AO 11t06ora 113 H11X, nepeXOAll no O'lepe- Al1 OT 0.QHOro MHOrayrOl1bHMKa K.Qpyra- My, CMelKHOMy CHMM. MHorayrol1bHHKl1, 113 KOTOpblX eoCTOllT MHOrarpaHHMK11, H33b1Bal0Tell rpaHRMH, MX CTOPOHbl - pe6paMH, a HX BBPWMHbl - BepWHHaMH MHOrorpaHHHKa. Ha p11cyHKe 8 np11ee.QeHbl HeKoTOpb1e np11- Mepb1 MHOrorpaHHl1KOB. OnpeAeneHMe. MHorarpaHHl1K Ha3b1eaeTc11 BblnYKflblM, ee1111 OH 11e>KMT no OAHY eTO- poHy OT n11oeKOeTM 11I060M era rpaHM. Illa aTOro onpe11e11eHM11 e11eAyeT, YTO see rpaHM BblnYKllOro MHOrorpaHHMKa llSl111- IOTCll n11oeKl1MM BblnYKl1blMM MHoroyro11b- HMKaMM. noeepxHOeTb BbmyK11ora MHOro- rpaHHMKa eoeTOMT M3 rpaHeM, KOTOpb1e 110- >KaT Bpa3HblX n11oeKOeTllX. npM 3TOM pe6- paMM MHOrorpaHHMKa 11811lllOTell eTOpOHbl MHOroyrOl1bHMKOB, sepwMH3MM MHOra- rpaHHMKa - sepwMHbl rpaHeM, n110CKl1MM yrnaMM MHOrorpaHHMKa - yrnbl MHOro- yral1bHl1KOB-rpaHeM. TeopeMa CMMOCOHa. 06b8M vnpl13MaTOl1,Qa MO>KHO Hai.irn no I cpopMy11e: V =- H(S1+4S+S2), 6 r.Qe H - era SbleOTa (paeeTOllHMe Me)f(,!ly n11oeKOeTllMl1 oeHOB3HMH), S, 11 S, - n110- Ua.Ql1 oeHOBaHl1M, s- nl10Ua.Qb cpeAHero ce~eHHR (eeYeH1111, napan11e11bHOra n11oe- Koer11M oeHo~aHMH 11 ,Qe1111Uero BbleOTY nono11aM). OnpeAeneHMe. BbmyK11blM MHorarpaHHMK, see sepwMHbl KOTOpora 11e>KaT s ABYX na- OnpeAeneHMe npaaMnbHoro MHororpaHHMKa Cpe,QM n11oeKl1X MHOrayra11bHMKOB oeo6oe Mecro 3aH11Ma10T npas1111b- Hb1e MHorayra11bH11K11. Cy111eeTsy10T 1111 «npas1111bHble MHOrarpaHH11Kl1», 11 'ITO 3TO TaKOe? Ellie B,QpesHeM rpeljl111 6bll111 M3BeeT- Hbl n11Tb YA11SMTel1bHblX MHorarpaH- H11KOB. OnpeAeneHMe. MHorarpaHHMK Ha3bl- eaeTe11 npaBHflbHblM, ee1111 see era rpaHM - paeHble Me)f(,!ly eo6oi1 npa- s1111bHb1e MHOrayra11bHl1Kl1, M3 Ka>K- AOM era sepWl1Hbl SblXOA11T OA11H3KO- BOe '111e110 pe6ep 11 see 11syrpaHHb1e yrnb1 pasHbl. TeopeMa. CyUeeTsyeT He 6011ee n11TM pa311H'IHblX BM.QOB npaSl111bHblX MHO- rarpaHHl1KOS. npaBMftbHble MHOrorpaHHMKM. 06o3Ha'leH1111: a - pe6po, H - sb1eo- Ta, s- nl10Ua.Qb noeepXHOeTH, v- o6beM, R- pa1111ye on11eaHHOH ecpe- pb1, r- pa.Q11ye en11eaHHOH ecpepbl. <l) @Ky6. Bee weeTb rpaHeH - Terpa3AJ1. Bee YeTb1pe 01T33AP. Bee BOeeMb Aone1a3np. Bee 12 rpa- MIOC33AP. Bee 20 rpa- KBil,lpaTbl. 111MeeT soeeMb rpaHH - paBHOeTOpOHHHe rpaHeH - paBHOeTOpOH- HeH - npasHnbHb1e n11rn- HeH- paBHOeTOPOHHHe sepwHH H12 pe6ep. TpeyronbHHKH. 111MeeT HHe TpeyronbHHKH. yronbHHKH. 111MeeT TpeyronbHHKH. 111MeeT YeTb1pe sepwHHbl H 111Meer weeTb sep- 20 sepwHH H30 pe6ep. 12 BepWHH H30 pe6ep. weeTb pe6ep. WHH H12 pe6ep. R =!!..J3 2 R= !!..J6 4 R =!!.J2 2 R =* (1+J5) .J3 R =* J 2(s+ J5) a r =I~ .J6 r =!!..J6 a R r =--Y.;-(3+J5)r= - r =4' 10+~2 6 ·d 4d S =6a2 S = a'.J3 S = 2a' .J3 S = 3a5(5~2d) S=5a' .,.3 V=a' a' re V- a' -:i-V=u..,2 11· a' t--=-== I ' - :a' (' :)- 3 , _ ==~ ,.: )- , ... -~ ~- I• nyeTb SA,A, ... A, - npaBMl1bH311 n-yral1bH3R nt1pa- Ml1,Qa. Bse.QeM e11e.QYIOUMe o6o3HaYeH1111: • a - yra11 HaKl10Ha 60KOSOra pe6pa Kn11oeKOeTM oe- HOBaH1111; {3- ,QByrpaHHblH yra11 np11 oeHOSaH1111; • y- n11oeKMi1 yra11 npM sepw11He; • 0 - ,QByrpaHHbliii yra11 np11 60KOSOM pe6pe. Tor,Qa enpaBeAJ111Sbl eOOTHOWeH1111: tga =cos*·tg13; sin l cosa= - -2 · . n ' sm 2 sina= ctg* ·ctg~ ; cos 13 =ctg-Ji- ·tg1 ; y cos-Ji- cos_§_ cos - = --· sinl3 =--2 2 sin_§_ ' sin-J} · 2 l1Hcf>OpMa1.1110HHO-cnpaeo<1HaR rn611111.1a ""0 0
  • 40.
    HH4'0n/ACT TM www.infoplast.ru nyTeBOAMTellb no'f8CTR M p e'fM --------.....lr1M~ CylleCTBLitTe/lbHOe 8HMMaH11e! Bee eyl4eeTs1.nenbHb1e B HeMe4KoM Sl3b1Ke n111wyTeSl e 3arnaBHOl1 6yKBbL. HeMe4K111e eyl1jeeTBlllTenbHble eKnOHSllOTefl no YeTbLpeM naAe>KaM. Cyl4eeTBlllTenbHoe B 111MeH111TenbHOM naAe>Ke (Nominativ) eny>1<111T B npeAnO>KeH111111 noAne>KaL4111M, B BlllHlllTenbHOM (Akkusativ)- npSlMblM 111n111 KOeBeHHbLM AOnonHeHllleM, B AaTenbHOM (Oativ) - TOnbKO KOeBeHHbLM AOnonHeHlll- eM. PoA111TenbHb1l1 (Genitiv) naAe>K o6o- 3Ha'-LaeT np111HaAne>KHOeTb; eyl4eeTBlllTenb- HOe B POAlllTenbHOM naAe>Ke, KaK npas111no, eny>1<111T B npeAnO>KeH111111 onpeAeneH111eM. POA HeMe4K111e eyl4eeTB111TenbHb1e 6b1sa10T My>KeKoro, >KeHeKoro 111 epeAHero POAa. noKa3aTeneM POAa eny>1<111T onpeAeneH- HbLl1 aprnKnb der (M.), die (>K.), das (e.). K JKeHCKOMY POAY. KaK npae1mo, OTHO- CRTCR cy1.1.1ecTBMTenbHble: 1.06o3Ha'-LalOL4111e n1114 >KeHeKoro nona (B TOM '-Llllene lllMelOL4111e eycpcp111Ke >KeHeKoro poAa - in: die Frau, die Spanierin, die Chemikerin). 2. EionbWlllHerno eyl4eeTBlllTenbHblX, 111Me- 10L4lllX oKOH'-LaH111e -e: die Kirche, die Buehne, die Kontrolle. Cyl4eeTBlllTenbHble, OKaH'-LlllBIOL4111eefl Ha - ion, -heit, -keit, -schaft, -taet, -ung, - ur, -ie, -ik, -enz, -ei, -anz: die Revolution, die Freiheit, die Taetigkeit, die Freundschaft, die Universitaet, die Zeitung, die Kultur, die Demokratie, die Physik, die Konferenz, die Arznei, die Bilanz. K MYJKCKOMY POAY. KaK npae11no, OTHO- CRTCR cy1.1.1ecTBMTenbHble: 1. 06o3Ha'-LalOL4111e n1114 My>KeKoro nona: der Mann, der Junge, der Professor, der Spanier. 2. Cyl4eeTB111TenbHb1e, 06pa3osaHHb1e e noMOL4blO eycpcp111Kea -er OT rnaronos: der Maler, der Schneider, der Lehrer. 3. Ha3BaHlllSl BpeMeH roAa, MBeH4es Ill AHei1 HeAen111: der Sommer, der April, der Sonntag. 4. Cyl4eeTB111TenbHb1e, 0KaH'-LlllBa10L4111ern Ha eycpcp111Ke -en, -ig, -ling, -or, -us: der Ofen, der Honig, der Fruehling, der Direktor, der Kommunismus. K cpeAHeMy POAY 06bl'fHO OTHOCRTCR: 1. EionbWlllHeTBO eyl4eeTBlllTenbHblX, OKaH- '-LlllBalOL4111XeSl Ha eycpcp111Ke -tum: das Christentum. 2. lllHcplllHlllTlllBbl rnaronoB B cpyHKL..1111111 ey- L48eTBlllTenbHOro: das Lemen, das Lesen. 3. Cyl4eeTB111TenbHb1e e yMeHbW111TenbHb1M111 eycpcp111KeaM111 -chen, -lein, a TaK>Ke e eycpcp111KeaM111 -ment, -um: das Kaninchen, das Tischlein, das Monument, das Datum. BHMMaHMe! Cyl4eeTB111TenbHb1e das Maedehen, das Fraeulein, das Weib OTHOef!TeSl K epeAHeMy POAY· MHo>KecTeeHHoe 'fMcno Mtto>1<eeTBBHHoe '-1111eno HeMe4K111x eyl4eeT- BlllTenbHblX 06pa3yeTeSl: ,QnH >KeHeKoro POAa - e noMOl.4blO eycpcp111- Keos -en, -n: die Kirche - die Kirchen, die Uebung - die Uebungen. ,QnH My>KeKoro 111 epeAHero POAa - e noMo- l.4blO eycpcp111KeOB - er, -e. np111 A06asneHllllll eycpcp111Kea -er KOpHeBb1e rnaeHb1e a, o, u, au np111H111Ma10T yMnHyT: der Tisch - die Tische; der Buch - die Buecher. Cyl4eern111TenbHb1e My>KeKoro 111 epeAHero POAa, 0KaH'-L111Ba10L4llleef! Ha -er, He 1113Me- Hfll0Tefl n11160 nplllHlllMalOT yMnflYT B KOpHe: der Bruder - die Brueder; das Fenster - die Fenster. CKnOHeHMe 11MeH cy1.1.1ecTe11TenbHb1X B eAlllHeTBeHHOM '-1111ene pa3n111'-La10T e111nb- Hoe eKnOHeH111e, ena6oe eKnOHeHl!le Ill >KeH- eKoe eKnOHeHl!le. Bo MHO>KeeTBeHHOM '-Lllle- ne see CYL4eCTBlllTenbHble CKnOHSllOTCSl no OAHOMY rnny. CMnbHOe CKnOHeH11e K ClllnbHOMY CKnOHeHllllO OTHOClllTCSl 6onb- WaSl '-LaCTb cyl4eCTB111TenbHblX My>KcKoro POAa Ill Bee - cpeAHero POAa. Maskulinum Neuter Norn. der Lehrer, der Platz das Fenster, das Kind desGen. des Lehrer-s, Fensters, des Platz-es des Kind-es dem Platz dem Lehrer, Oat. dem Lehrer, dem Kind Akk. den Lehrer, den Platz den Lehrer, den Kind Cna6oe cKnoHeH11e K cna6oMy CKnOHeHllllO OTHOCSlTCSl CYL4eCT- BlllTenbHble My>KcKoro POAa, 0KaH'-LlllBa10- L4lllecH Ha -e, a TaK>Ke Ha cycpcplllKCbl lllHO- CTpaHHOro npOlllCXO>KAeHlllSl -ist, -ent, -ad, -et, -nom. BHMMaHMe! Cyl4eCTB111TenbHbie der Held, der Hirt, der Herr, der Mensch, der Baer TaK>Ke OTHOCSlTeSl K cna6oMy CKnoHeHllllO. Norn. Gen. Oat. Akk. der Genosse, der Held des Genossen, des Heiden dem Genossen, dem Heiden den Genossen, den Heiden >KeHCKOe CKnOHeHMe K >KeHCKOMY eKnOHeHllllO OTHOeSlTCSl see CYL4eCTBlllTenbble >KeHCKOro POAa. n3Ae>K- Hble OKOH'-LaHlllSl B 3TOM Tlllne CKnOHeHlllSl OTCYTCTBYIOT. AprnKllb Bee aprnKn111 cornacy10TeH e cyl4eCTB111- TenbHb1M111 no naAe>KaM, POAaM 111 '-LlllenaM. OnpeAeneHHblM apTMKnb ynoTpe6nHeTCSl c 111c'-L111cnHeMb1M111 cyL4eCTB111TenbHb1M111 B eAlllHCTBeHHOM 111 MHO>KeCTBeHHOM '-Llllcne, a TaK>Ke c tte111e'-1111CnHeMb1M111 cyl4eCTBlllTenb- HblMlll. Oni>eAeneHHblM apTMKJlb np111MeHHeTef!, ecm1npeAME!T113aecTeH roaopS1L4BMY. 4BCTb 1 ynoM111HaneH pattee 111n111 HBnHeTCSl BAlllHeT- seHHblM B eaoeM poAe, a TaK>Ke ecn111 ne- PBA eyl4eeTBlllTenbHblM CTOlllT np111nara- TenbHoe B npeBOCXOAHOl1 CTeneHlll lllJllll no- PSlAKOBOe '-L111en111TenbHOe (der beste Schueler, das erste Jahr). HeonpeAeneHHblM apTMKnb ynoTpe6nH- eTCSl TOnbKO e 111c'-L111CnfleMblMlll eyl1jeCTBlll- TenbHblMlll B eAlllHCTBeHHOM '-LlllCne, ecn111 npeAMeT Helll3BeCTeH roBOPSll4eMy. Dort steht ein Maedchen. Das Maedchen ist noch ganz klein. CKnoHeHMe apTMKnelli OnpeAeneHHb1iil apT11Knb My>K. p. >KeH. p. Cp. p. MH. 'f. Norn. der die das die Gen. des der des der Oat. dem der dem den Akk. den die das die Bo MHO>KeCTBeHHOM '-LlllCne aprnKnlll CKnO- HSllOTCSl OAlllHaKoso He3aa111c111Mo OT poAa. HeonpeAeneHHbliil apTMKnb My>K. p. >KeH. p. Cp. p. Norn. ein eine ein Gen. eines einer eines Oat. einem einer einem Akk. einen eine ein JlW·IHble MeCTOLitMeHLit~ n111'-1Hble MeCTOlllMeHlllSl B HeMe4KOM Sl3b1Ke 1113MeHHIOTCSl no naAe>KaM 111 '-LlllCnaM. EA. 'f. ich- fl dU-Tbl er-OH sie - oHa es - OHO Nominativ MH. 'f. wir- Mbl ihr- Bbl (MH.'-Lllleno OT «Tbl») sie - OHlll Sie - Bbl (se>1<n111saH cpopMa) BHMMaH11e! MecrnMett111e Sie, o6o3Ha'-Lal0- L4ee Be>KnlllBYIO cpopMy o6paL4eHlllSl «Bbl», B HeMe4KoM Sl3b1Ke scerAa n111weTcf! c 3a- rnasttol1 6yKBbl, B 0Tn111'-L111e OT pyccKoro, rAe 3arnasttaf! 6yKsa ynoTpe6nHeTCSl TOnbKO B nlllCbMax. ich-meiner du -deiner er- seiner sie - ihrer es -seiner ich- mir du-dir er-ihm sie -ihr es-ihm ich-mich du - dich er - ihn sie-sie es- es Genitiv Oativ Akkusativ wir- unser ihr- euer sie -ihrer sie - lhrer wir - uns ihr - euch sie- ihnen Sie - Ihnen wir - uns ihr - euch sie - sie Sie - Sie
  • 41.
    np1maraTe/1bHble HeMe4K1-1e np1-111araTe11bHb1e comacyioTCRc cy1J.1eCTB"1T011bHblM"1 no POAaM, n~ell<aM "1 4"1CllaM. CKnOHeHMe npMnaraTenbHblX Cna6oe cKnoHeHMe, eAMHCTBeHHoe '4Mcno (onpeAeneHHblM apTMKnb) My>K. p. >KeH. p. Cp. p. Nom. der alte Mann die alte Frau das kleine Kind Gen. des a/ten Mannes der a/ten Frau des kleinen Kindes Oat. dem a/ten Mann der a/ten Frau dem kleinen Kind Akk. den a/ten Mann die alte Frau das kleine Kind Cna6oe CKnoHeHMe, MHO)l(eCTeeHHOe '4MCno (onpeAeneHHblM apTMKnb) My>K. p. >KeH. p. Cp. p. Nom. die a/ten die a/ten die Maenner Frauen kleinen Kinder Gen. der a/ten der a/ten der Maenner Frauen kleinen Kinder Oat. den a/ten den a/ten den Maennern Frauen kleinen indern Akk. die alten die alten die Maenner Frauen kleinen Kinder CMnbHoe CKnoHeHMe, eAMHCTBeHHoe '4Mcno: (HeonpeAeneHHblii apTMKnb) My)I(. p. >KeH. p. Cp. p. Nom. ein alter eine alte ein kleines Mann Frau Kind Gen. eines alten einer alten eines Mannes Frau kleinen Kindes Oat. einem alten einer alten einem Mann Frau kleinen Kind Akk. einen alten eine alte ein kleines Mann Frau Kind CMnbHOe CKnOHeHMe, 9AMHCTBeHHOe '4Mcno (6e3 apTMKni:1) Nom. harter Stein rote Jacke frisches Wasser Gen. hartes Steines roter Jacke frischen Wasser Oat. hartem Stein roter Jacke frischem Wasser Akk. harten Stein rote Jacke frisches Wasser CMnbHOe CKnOHeHMe, MHO>KeCTBeHHOe '4MCno (6e3 apTMKnl'I) MyJK. p. >KeH. p. Cp. p. frischeNom. harte Steine rote Jacken Wasser Gen. harten Steines rater Jacken frischen Wasser Oat. hartem Stein rater Jacke frischem Wasser Akk. harten Steinen rote Jacke frisches Wasser npMTl'l>K8TenbHble M9CTOMM9HMl'I np"1TR)l(aTellbHbl0 M0CT0"1M0H"1R comacylOT- CR c cy1J.1eCTB"1TellbHblM"1 no POAaM, n~e- )l(aM .,, 4"1CllaM. ich-mein du-dein er, es - sein, dessen sie - ihr, deren wir- unser ihr- euer sie - ihr, deren Sie- lhr 8HMM8HHe! np1-111araT011bH00 np1-1MaeT n~0)1(Hbl0 OKOH- 4aH"10 C"111bHOrO CK110H0H"1R, 0C11"1 n0p0A H"1M CT0"1T 1110600 npHrnll<aT011bH00 M0CTO- HM0HH0 111-160 OTpH4aT011bH00 M0CTOHM0HH0 kein. n p1o111araT011bH00 npHHHMaeT naA0)1(Hb10 OKOH4aHHR c11a6oro CK110H0HHR, 0C11"1 n0p0A H"1M CTOHT OAHO "13 C110AYIOIJ.1HX yKa3aT011b- HblX M0CT0"1M0H"1iii, H3M0HRIOLJ.HXCR no rnny onp0A0110HHoro aprnK11R: dieser 3TOT jener TOT jeder Ka)l(Abliii mancher H0KOTOpbliii solcher TaKOiii welcher KOTOpbliii r11aro11 HeMe4K1-1iii maro11 H3M0HR0TCR no 111o14aM H 4HCllaM. 11H'4Hbl9 OKOH'48HMl'I rnarona: fA.'4. MH.'4. 1 n. 2n. 3n. -e -st -t -en -t -en 0CHOBHbl0 cj>opMbl maro11a: HHQlHHHTHB, Q>opMa npocToro npoweAwero speMeH1-1 (lmperfekt) H np1o14acrne npoweAwero spe- MeH1-1 (Partizip II). C11a6b1e maro11b1 npHHHMalOT OKOH4aH1-1e -te B lmperfekt H -t s Partizip II: tanzen - tanzte - getanzt sagen - sagte - gesagt C1o111bHb10 maro11b1 1-1Me10T 4ep0AOBaH1o1e KOpH0BblX maCHblX B pa3HblX Q>opMax ... OKOH4aH1-10 -en s Partizip II. singen - sang - gesungen finden - fand - gefunden BcnoMoraTenbHble rnaronb1 B H0M04KOM R3blK0 TpH BCnOMOraT011bHblX maro11a: sein, haben, werden, c11y)l(a1J.11-10 A11R 06pa3oeaH"1R CllO)l(HblX Q>opM. Cnpsi>1<eH1o1e ecnoMorarenbHblX rnaronoe: HacTosi114ee epeMR sein haben werden ich bin habe werde du bist hast wirst er, sie, es ist hat wird wir sind haben werden ihr seid habt werset sie, Sie sind haben werden npoWeAwee epeMR ich war hatte wurde du warst hattest wurdest er, sie, es war hatte wurde wir waren, hatten, wurden ihr wart hattet wurdet sie, Sie waren hatten wurden BpeMeHa rnarona HacToR114ee epeMR (Praesenz) 06o3Ha4a0T A0iiiCTBH0 np1-1eb14H00, nocrn- RHH00 "111"1 npOHCXOARIJ.100 B AaHHbliii MO- M0HT. 06pa3y0TCR np1-16ae110HH0M 11H4Hb1X OKOH4aHHiii K OCHOB0 maro11a: ich tanze wir tanzen du tanzt ihr tanzt er, sie, es tanzt sie, Sie tanzen npocToe npoWBAWH (lmperfekt) YnoTpe611ReTCR B OCHOBHOM B nHCbM0HHoM pe4H HllH B nOC110AOBaT0llbHOM noeecTBOBa- HHH AflR 00o3H840HHR AeMCTBHM, npoMCXO- AMBWMX B npowJIOM. rloKa3aT011b lmperfek.t y c11a6blx r.narollOB - ~c te- . CT~ OCHOBOiil Iii OKOtf'latMBll y CMl1bHblX - YepeAOBaHHe KOpHeeoro macHoro. ich sagte, sang du sagtest sangst er, sie, es sagte, sang gen wir sagten, sangen ihr sagtet sanget sie, Sie sagten, san- npoweAwee coeepweHHoe (Perfekt) 06o3Ha4aeT AeiiicTBH0, coeepw0HH00 B npOWllOM. 06pa3y0TCR c noMOLJ.blO BCnOMO- raT011bHOro maro11a haben e 11H4HOiii Q>opMe HaCTOR1J.1ero epeMeHH + Partizip II CMb1c110- eoro maro11a. ich habe gesagt du hast gesagt wir haben gesagt ihr habt gesagt er, sie, es hat gesagt sie, Sie haben gesagt 8HMM8HMe! c maro11aM"1, 0603Ha4alOIJ.1"1M"1 AB"1)1(0H"10 HllH H3M0H0HH0 COCTORHHR B Perfekt ynoTpe611ReTCR enoMoraTe11bHb1iii maro11 sein. ich bin geflogen du bist geflogen wir sind geflogen ihr seid geflogen er, sie, es ist geflogen sie, Sie sind geflogen nmocKeaMnep<t>eKT (Plusquamperfekt) 3TO ep0MR o6o3Ha4a0T A0iiiCTBHR, 3ae0p- W0HHbl0 B npOWllOM "111"1 np0AW0CTBOBaB- WH0 APYrHM A0iiiCTBHRM e npow110M. 06pa- 3y0TCR c nOMOLJ.blO BCnOMOraT011bHOro ma- ro11a haben (AllR maro11os, o6o3Ha4al0Ll.HX ABHll<0HH0 .,, "13M0H0HH0 COCTORHHR - sein) B 11"14HOiii Q>opMe npoweAwero ep0M0HH nlllOC Partizip II CMb1c11oeoro maro11a. ich hatte gesagt wir hatten gesagt du hattest gesagt ihr hattet gesagt er, sie, es hatte gesagt sie, Sie hatten gesagt ich war geflogen wir waren geflogen du warst geflogen ihr wart geflogen er, sie, es war geflogen sie, Sie waren geflo- gen 6y,qy114ee epeMR (Futurum I) 0603Ha4a0T A0iiiCTBH0, KOTOp00 np0"130iii- A0T e 6YAYIJ.10M. 06pa3y0TCR c noMOLJ.blO ecnoMoraT011bHoro maro11a werden e 11"14- Hoiii Q>opMe + MHcj>MHMTMB CMblCllOBOro ma- ro11a ich werde gehen du wirst gehen er, sie, es wird gehen gehen wir werden gehen ihr werdet gehen sie, Sie werden 6YAYL14ee e npoweAWeM 06o3Ha4a0T A0iiicTe1o10, KOTopo0 3ae0pwHT- CR B 6YAYLJ.0M, 111-160 np0An0110)1(HT011bH00 A0iiiCTBH0 e npow110M. 06pa3y0TCR c noMo- LJ.blO ecnoMoraT011bHOro maro11a werden e 11"14Hoiii Q>opMe + Partizip II CMb1c11oeoro maro11a + MHcj>MHMTMB ecnoMoraTenbHoro rnarona haben (Sein). ich werde geschrieben haben du wirst geschrieben haben er, sie, es wird geschrieben haben wir werden geschrieben haben ihr werdet geschrieben haben sie, Sie werden geschrieben haben 11HtPOPMB4MOHHO-cnpaa04HBR ra6nM4a N r- © 0 00 •l1HtPonnacr ", 2003 119180 r. MOCKBB, yn. 6. nonRHKa, ll· 24, ren.: (095) 230- 0608109, tPBKc; (095) 230-7111 N 0 .,., 0 0 0 r- 0 0 1D
  • 42.
    www.infoplast.ru Cnoeapb noeceAHeeHoroo6~eHMSI -------.....0Ae>KAa Die Kleidung CKOllbKO CTOl1T ..? KaKoM y sac pa3Mep? 6e11be 60COHO>KKl1 60Tl1HK11 6t0CTrallbTep raflCTYK AeweebtM A>K11HCbl AOporoM, -afl 30HT wanKa KO>Ka KOllfOTKl1 KOCTIOM KOWeneK Kpy>KeBO KynallbH11K KYPTKa HOCKl1 HOYHafl py6awKa nanbTO nepYaTK11 n11>KaMa nnaTbe n11aU1- AO>KAeB11K nOflC pa3Mep py6awKa pyKaB CBl1Tep CYMKa TycjJ1111 QJYT6011Ka wapcjJ we11K wepCTb w11flna wopTbl I06Ka Wieviel kostet. ..? Welche Groesse haben Sie? die Waesche die Sandaletten die Halbstiefel der Buestenhalter die Kravatte bi/lig die Jeans teuer der Regenschirm die Muetze Leder die Strumpfhose der Anzug (My>KcKoii); das Kostuem (>KeHcK11ii) die Geldboerse die Spitze der Badeanzug dieJacke die Socken das Nachthemd der Mantel die Handschuhe der Sch/afanzug das Kleid der Regenmantel der Gurt (Gurtelj die Groesse das Hemd der Aermel der Pullover die Tasche die Schuhe das T-shirt das Halstuch die Seide die Wolle derHut die Shorts der Rock '-'eern Die Farben 6e>KeBbtM beige 6e11btM weiss >KellTblM gelb 3e11eHbtM gruen KOp11YHeBblM braun KpaCHblM rot opaH>KeBblM orange p030BblM rose CBeTllblM hell cepbtM grau Cl1Hl1M blau TeMHblM dunkel QJ110110TOBblM violet!; Ii/a ciepHblM schwarz AeHbrH, 6aHK, noKynKH Das Geld. Der Bank. Kaufen CKOllbKO 3TO CT011T? 5'I 6bl XOTell... no>Ka1iyMcTa 3To AOporo! nOAaBaTb >Kano6y o6Halll1'-111Tb YeK 3aKa3aTb on11aTl1Tb CYeT 6anaHc Wieviel kostet es? /ch moechte... bitte Das ist teuer! sich beschweren einen Scheck einlosen bestellen die Rechnung begleichen die B lanz 6aHKOBCK11M CYeT das Konto AaTa nnaTe>Ka der Zahlungstermin AeHbrl1 das Geld AOCTaBKa die Lieferung Kacca die Kasse Kacc11p (a 6aHKe) der Kassier KOMaHA11POBKa die Dienstreise KpeAl1TKa die Kreditkarte Kypc (BMIOTbl) der Wechselkurs MellO'-lb das Kleingeld HM11'-1Hble das Barge/d Hanor Steuer 0611araTb HanoroM besteuern o6MeHHblM nyHKT Wechselstelle onnaTa die Bezahlung OTAen npOAa>K die Verkaufsabteilung nepeBOA11Tb AeHbrn das Geld ueberweisen nl1CbMeHHO schriftlich noKynaTellb der Kaeufer npOAaBaTb verkaufen np0Aaee4 der Verkaeufer npo4eHT dieZinsen pacnpOAa>Ka der Ausverkauf paCXOAbl die Ausgaben; die Kosten peK11aMa411fl die Reclamation c6epe>KeH11fl die Ersparnisse ccieT (3a noKynKy, die Rechnung ycnyry) TaMO>KHfl dasZollamt TOproBllfl der Handel TpaTbl die Ausgaben yH11eepMar der Kaufhof yc110011flAOCTa0K11 Lieferungsbedingugen yc110011fl on11aTb1 Bezahlungsbedingungen 4eHa der Preis 4eHHOCTb der Wert 3KOHOMl1Tb (AeHbf11) das Geld sparen 3Aopoebe Die Gesundheit aHTl16110Tl1K aHrnHa aHTl1CenTl1K anTeKa 6011e3Hb 6011b e ropne 60llb 6pOHXl1T spay rnnc rp~yCH11K rp11nn A11arH03 3y6Hafl 60llb l1HQJeK4l1fl Kan1111 Kawenb KpOBb neKapCTBO Ma3b M11KCTypa (OT KaWllfl) HeceapeH11e>Ke11yAKa O>KOr onyxw11M na411eHT npOCTYAa COllHe'-IHblM O>KOr cpeACTBO TBMnepaTypa (BblCOKafl) TOWHOTa TpaBS'lHOM YaM YKOll das Antibiotikum dieAngine Antiseptikum die Apotheke die Krankheit Halsschmerzen derSchmerz die Bronchitis der Arzt das Pf/aster das Thermometer die Grippe die Diagnose Zahnschmerzen die lntektion die Tropfen der Husten das Blut die Arznei die Sa/be die Hustenmixtur Verdauungsstorung die Brandwunde geschwollen der Kranke die Erkaeltung das Rezept die Sonnenbrandwunde das Hei/mittel der Fieber die Uebelkeit der Kraeutertee die lnjektion 48CTb 2 YYe6a, pa6oTa Das Studium, die Arbeit YYl1T0Cb! Pa6oTaMTe! YYl1TbCfl a ey3e no cne411anbHOCT11... Studieren Sie! Arbeiten Sie! (ein Fach) studieren 3apa6aTbtBaTb AeHbrn Geld verdienen npoXOA11Tb Kypc (no...) einen Kursus durchmachen 6yxranTep der Buchhalter 6yxramepcK11M yYeT die Buchfuehrung peK11aMa die Reklame ryMaH11TapHbte HayK11 die Geisteswissenschaften KH11ra KHl1>KHblM Mara311H 6113Hec-06yYeH11e KaMnyc Kapbepa KOnnera KOllfleA>K 11HQJOpMaTl1Ka Kypc cTeneHb cnoeapb 06pa300aH11e 3H411KllOneA11fl 3K3aMeH cj:Ja6p11Ka 11306pa311T01lbHOe 11CKYCCTBO das Buch die Buchhandlung Ausbildung in Kommerz DerKampus die Kariere; die Laufbahn der Kollege; die Kollegin Der College die lnformatik derKursus der (akademische) Grad das Woerterbuch die Bi/dung die Enzyklopaedie die lmmatrikulation die Pruefung die Fabrik der bildende Kunst 11HocTpaHHb1e fl3blK11 die Fremdsprachen AHBBHOe (OTABfleH11e, das Direktstudium 06yYeH11e) 04eHKa MeCTO pa60Tbl npaeo iop11A11YecK11M cjJaKyllbTBT 611611110T0Ka die Note dieArbeit dasJura die juristische Fakultaet die Bibliothek cne411a11113a411fl die Spezia/isierung ecTecrneHHbre HayK11 die Naturwissenschafte eeYepHee (OTAeneH11e, abend 06yYeH11e) npenoAaBaTenb AOKll~ pacn11caH11e WKOna 3aHS'lTl1fl pa6oTa no11Hafl 3aHS'lTOCTb YaCTl1'-1Hafl 3aHflTOCTb der Dozent, der Lektor Der Vortrag der Stundenplan die Schute dieStudien dieArbeit die Vollbeschaftigung die Tei/beschaftigung EAa, pecTOpaH Das Essen, das Restaurant 5'! 6b1 xoTen... /ch moechte... 5'I 6b1 xoTen 3aKa3aTb... /ch moechte bestellen... CYeT, no>KanyMcrn! Die Rechnung, bitte! 3a CTOllOM Am Tisch Bl111Ka der Gabel ropci114a der Senf >KapeHafl KapTOWKa die Bratkartoffeln 3aBTpaK der Fruehstueck 3aKyCKa die Vorspeise Maeno die Butter HO>K der Messer nepe4 der Pfeffer np11eM n11U111 die Speise pacT11TellbHOe Maeno das Oel cancjJeTKa die Serviette COllb das Salz cne41111 die Gewuerze CTaKaH das Glas Cb1p die Kaese
  • 43.
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MocKaa, Kaw11pcKoe wocce, 21 E-mait mail@infoplast ru Http:llwww.infoplast ru Ten.: (095) 320-94-89 Cl>aKc: (095) 320-94-88 d, 00 N 0
  • 44.
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  • 45.
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  • 46.
    Ol5PA30BAHME ..., PYeGKHH A3blK -------.... ·'!MK· nocne cornaCHblX 0-m3-C )/( zpy;J.4ui< nepenuQ4Ui< p83eeQ4ui< nepe6e}!{<fcii< 8emoM8filtiUK -------.... - ll.IMK - B OCTanbHblX cnyYaHX CycpcpVIKCbl -etc-HK- Ecn1-1 np1-1 CKnOHeHHH cnoea rnacHaH cy¢>¢>1-1Kca Bbma,qaeT He Bbma,qaeT ,,......_ ,,......_ - eK - - MK - Cb/H04K8 - Cb/H04eK KUpnU4UK8 - KUpnu4[jK - ;;;-..__ 38M04K8 - 38M04f1K K8p8H08WUK8 - K8p8H08WUK Cy<l><l>VIKCbt -'K- VI -CIC- e VIMeHax npV1naraTenbHbtX ,.... - K - - Ci<- 1. B np1-1naraTenbHblX, Bo ecex ocranbHblX HMelOl.J..IHX KpaTKylO cpopMy np1-1naraTenbHblX BR30K - 6R3KUU </Jp8H4Y3CKuii pe30K - pe3Kuii ,,..... M8mpoccKuii U/OflbCK UU 2. B np1-1naraTenbHblX, 06pa3oeaHHblX OT cyl.J..I . C OCHOBOH Ha -K - 4, - 4 HeMe4 - HeMe U U mypoK - mype4'Kuii mKa4 - mK84KUU Cy<l><1>MKCbl -0-3- y Hape'fMM c npVICTaeKaMVI Vl3-, AO-, c -a- - 0 - Ecm1 Hapel.l1-1e o6pa3oeaHo OT OT np1-1naraTenbHOro, B 6ecnpHCTaBO'-lHOf0 KOTOpOM y>Ke 6blnH npHCTaBKH np1-1naraTenbHOro OOX004U60 +--- aDX004U6b/U lao8eHa .._ o8eHuii ucnyz8HH8 +--- ucnyZ8HHb/U oocb1m8 +--- Cb1mb1ii B HapeYHHX, o6pa30BaHHblX c cnee8 +--- neeb1ii ,qpyrnMH npHCTaBKaMH Hciznyxo +-- znyxoii fineeo +--- neeb1ii rnaCHbre e 6e3y~b1x cycpcpVIKcax rnaronoe -oea- (-eea-), -biBa- Hrna-) - Osa - (- eBa -) -biBa - (- Hea -) rnaron 1 n., e,Q.Y. HaCT. HnH 6y,Q . rnaron 1 n., e,Q.Y . HaCT. 11n11 6y,Q . BpeMeHM OKaHYMBaeTCH Ha -y/O (-IOIO} epeMeHH OKaHYMBaeTCH Ha -b/68/0 (-Ue8/0) nocoeemw (1 n ., eo.4., 6yo.ep.) noyKn8ob1e810 (1 n., eo.4., 6yo.ep.) - coeemoeamb mpe6Y!Q (1 n., eo.4., H8Cm.ep.) - mpe6oeamb M8fl/O/O (1 fl., eo.4., H8Cm.ep.) -Maneaamb - noyKn8obtiiamb p8CCK83blB8/0 (1 n., eo.4., H8cm.ep.) ------ p8CCK83b/B8mb p83ZOB8pUB8/0 (1 fl., e0.4., H8Cm.ep.) - pa3zoeapfiiiamb 06pa30BaHVle VI cy<l><l>VIKCbl npVl'iaCTVIH Cos. Hecoe. nepe- Henepe- CnpH>K. Cycj:>cj:>MKCbl BM,Q XO,QH. XO,QH. mar. I + + + II + + + + I, II CTpa,q.HaCT.Bp. I + + II CTpa,q.npow.sp. + + + I, II 06pa3oeaHV1e VI cycpcpVIKCbl AeenpVl'iaCTVIH ~T Coeepw. Hecoeepw. Cycj:>cj:>. np11Mepb1 r. np1-14acrnR BM,Q BM,Q ,Qeenp. rnaronb1 ,Qeenp11yacrnH OT OCHOBbl --a - npOYMTaTb npOYMTa~ Heonp. -tiliM- 3a6ny,QMTbCH 3a6ny,q11Bi:i:mcb .Qeenp1-1yacT11e ctJOpMbl - tiJj;f - ,,......_ ysneYb vsneKWM COB. BM,Qa OT OCHOBbl --a-npocTOro (-R-) npHl.J..IYPfillcH npHl.J..IYPRCb 6y,Q. ep. .Qeenp11YaCT11e OT OCHOBbl KPH~ KpMYa,.... CTY T CTyY'ci- a - HeCOB. BH,Qa HaCT. - 5l' - ynb16ajQ]CH ynb16af!cb epeMeHM CMJl'ITT! CM.QR 3anOMHMTb! 6b1Tb - 6y,Q~ H MHH B cyQ><1>MKCax pa3HblX liaCTeM peliM - H - • HH • np1-1naraTenbHbl0 1. 06pa3oeaHHble OT cyll.eCTBHTenbHblX ,,..... ,,-.... -€HH- conoMeHFib1ii- aH - KO>K8Hb/U ----- ---,,-.... flbHRHOii · OHH - cmaH4UOHHb/U-RH · -Gil - 2ycUHb1ii OT CYU· C OCHOBOH Ha H -------~nyHa - nyHHbl U onoe'fiHi:ib1ii 1!1CKJllO'-l0HHR: ,,..... cmeKnRHHblii eempeHblii depee°fiHi:rb1ii 2 . Ha - OBaHHblH ' - eBaHHblH B cnoeaX-HCKJllO'-l0HHRX MapuHoeaffi:ib1e 02yp4b1 Ko6aHb1i1 myweeaHi'b1ii nucm 5KiiaaHblii accjJanbmupoeaHl?oe wocce 3 . Cne,ll yeT 3anoMHHTb CMb/Wne b/U pe6eHOK >Kena Hblii HaJea bli16pam Heeuda.- blii noca>KeHblii ome4 HBCflblxa;:/i;b/U Heaada b1i1 HBJKda b1i1 He4uma b1i1 '-lfNaR ii - H. - HH • 4. OTrnaronbHble np1-1naraTenbHb1e o6pa30BaHHbl0 OT 06pa3oeaHHb1e nYTeM rnarona Hecoe. BH,Qa nepexo,Qa O,QHOH l.lacrn pell1>1 6e3 npHCTaBKH B ,Qpyryto (H3 nplilllaCTlllH B Me'leiib1u - Memumb nepeHOCHOM CMblCne) B pea'Hb1u - pea'lnb nonHOH Iii KpaTKOH cpopMe i11CKJllO'-l0HfllR'. 02paHU4eHHb1ii 'lenoeeK KOH'leHblii ('lenoeeK) - (Komopb1ii Mano pa3eum, KOH°'lumb HedaneKuii) npou.iiiiioe (eocKpeceHbe) - oapai-lu'leHHaR meppumopuR "' ----npocmumb nneMR oapaHU'IBHHO • H. 5. B 3Ha'-leH111111 «BblCOKaR cTeneHb Ka'-leCTBa» HOWeHoe - nepeHoweHoe cmupaHoe - nepecmupaHoe 6. B cnO>KHblX cnoeax [(eiibHoi(jXJeHb/U MiinoeJ>Ke.,aR Ceeii<eMopoJKe bli1 CTPa.QaTenbHble np acnui npC>U.1e.qwero epe 0HM 11 B IJ)aT OH ¢lo e oopoza ·-- ~ ...... a - HH • CTpa,QaTe11bHb1e np111llaCT111R npowe,Qwero epeMeH111 a) Ha - oeaHHblH, - eeaHHblH + np111crneKa 11111111 3ae111c111Moe cnoeo U36anoeaHHblii 8 l/eM? ----.MapUHOBaHHOe e yKcyce 6) eCTb np111CTaBKa, KPOMe He- ~ ----Bb/MOUjeHHaR e) eCTb 3aBlllClllMOe CJlOBO ----~MOUjeHHaR KaMHeM r) 06pa3oeaHHb1e OT rnaronoe coeepw. 01-1,Qa 6e3 np111crneoK 6pocumb - 6poweHHb1ii ecmpemumb - ecmpe'leHHblii Hapell111R n11weTCR CTOnbKO , CKOJlbKO 6b1Jl0 e cy<Dq>11Kce np14nararenbHoro. OT IOTOPOrO o6pa30BaHO apey11e
  • 47.
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I -o B H83B8HIUl.X HaceneHHblX nyHKTOB Ha -UH. - blH. -oe, -ea, -UHO, -blHO, -060, -eeo n00 CapamoeQM. nOO KanR3UHOM naAe>KHble OKOH'"laHlllSI cy111ecTBl/ITenbHblX Ha -lllSI, -lllM, -Ille na,1:1e>K - HR - Hl1 - He P. n . - u - - A. n . -u - - n. n . -u - u -u -y, -IO -y, -/0 ~Wb -UWb ~m -um 1 n . ~M -UM 2 n. -eme -ume 3n. -ym, -/Om -am, -Rm rnaCHble 0 , A B OKOH'"laHlllSIX cy111ecTBlllTenbHblX c cy<1><1>111KCaM111 ?---.:... ........--..... ........--..... ...----.... "' -yWK-, -IOWK-, -blWK-, -lllWK-, -n- Ll1.n. eA.Y. -a -o Cy<t><t>HKC ---- __..._ ---- ----- YWK - IOWK - b/WK • UWK - OAyweeneHHble HeOAyweeneHHble cy111ecTe11TenbHb1e cy111ecTe11TenbHb1e My>K. 11 lt<eH. POAa Myll<. 11 cp. POAa oeoftUl@l OOMCiUJKQ] napHCiUJR'{fJ nonr61iii<g MamftU~ JepHblliJKQJ xne6ftUI@ Cy<t><t>HKC - fi - OAyweeneHHble cy111ecTe11renbHb1e cy111ecTe11TenbHb1e cp. POAa Myll<. 11 06L1-1ero po.Qa Jy6uffQJ Janpaeuffr!J MOl./ai7QJ Jy6pu{tgj rnaCHble E, Ill B OKOH'"laHlllSIX cy111ecTe111TenbHb1x -be, -be, - bff e 1. Cy1..4eCTBHTenbHOe cp. p. B n .n . eA.Y. e 6eJy,1:1apHOM nono>KeHHH: o cl./acm 2. B P.n . MHO>K.Y. (no,1:1 mapeHHeM HaY. cpopMa) py>Kb~ - py _u 2. B P.n. MHO>K.Y. (HaY. cpopMa 6e3 y,1:1apeHl1R) : wanyHbR - wanyH'ldf}_, l1HQJopMa4HOHHO-CnpaB04HaJI ra6nHqa Cl 000 •l1HQ1onnacr•, 2004 r. MocKBa, KawHpcKoe wocce. 21 E-mait ma11@mfoplastru H. · www.infoplastru
  • 48.
    OSPA30BAHME ..., PYGGKHH A3blK CrpaAarenbHble np114acrns:1npow. sp. OnnaronbHble np1111ararenbHb1e 1. CoxpaHs:1er maronbHOe 3Ha4eH11e, yKa3b1saer Ha speMeHHOe 1. He coxpaHs:1er maronbHOro 3Ha4eH11s:1, yKa3b1saer Ha nOCTOS'IHHblH COCTOS'IHl1e npl13HaK - Ka4eCTBO 2. lllMeer Karerop1110 speMeH11 2. He 11Meer Karerop1111 speMeH11 3. 0TBe4aer Ha sonpoc: c KomopbiM 'Imo coenanu? 3. 0TBe4aeT Ha BOnpOCbl: KBKOB? K8KOaa? K8KOBO? KBKOBbJ ? KBKOU? KBK8R? K8KOe? KaKue? 4. ECTb np11CTaBKa 111111 3aBl1C11MOe CJlOBO; o6pa3ylOTCS'I OT maronos cosepweHHoro B11Aa 6e3 np11crasK11: pew!itrb - 4. 06pa3yiorcH or maronos HecosepweHHoro B11Aa 6e3 H0C B npl1CTaBKl1 np11 OTCYTCTBl111 3aBl1Cl1MOro cnosa: nel./b - nel./eHb/U peweHHbtM 5. Ynorpe611s:1ercs:1 B nps:1MOM 3Ha4eH1111 5. Ynorpe611s:1ercs:1 B nepeHOCHOM 3Ha4eH1111 Mope~ (c o6pa30BaBWl1Ml1CS'I BOJlHaM11) OeBOl./KB ~ (HeCnOKOHHafl) l./enoaeK ~ (11cnb1Tb1Ba10LL111i:1 r pesory) zonoc ~ (HeCnOKOHHblH) nw.,io ~ (4enoseK, np1161111>1<eHHb1i:1 Ksnacrn) MbJCflU~ (6naropOAHble) np11Me4aH11e: MOlKHO nOA06paTb Cl1HOHl1M - np1111araTeJlbHOe 6. Ha - OBBHHblU, - eaaHHb/U (ec1111 eCTb npl1CTaBKa 11 3aBl1C11MOe 6. Ha - OBBHHbtU, - eaaHHb/U (ec1111 HeT np11CTaBKl1 11 3aBl1Cl1MOro CJlOBO) b nocne WMmllJ.4MX B pa3Hb1X Lf3CT.RX pelfM )f(eH. p. , 3 CKJl.: noMO£Mb, oo~b, 6pOfMb a) 2 Ill1LO, eA.4.: l./umaewb 6) Heonp. cpopMa: cmepe~b, 6epe~b He n11wercH a) My)f(.p., 2 CKJl.: flY':!, nejJJ, HOl/S. 6) MH. 4. , P.n .: c nne':!, MHOZO pOYJ, U3-3a my':! B KpaTKOH cpopMe: KOfl/O':!, cae]!i, xopo!J! rnaron B) nosem1Te11bHOe HaKJlOHeH11e: ompel!$,b, HBMBl!$,b a) nocne w 11 I./: cnnO!J!b, nocne >K: 3BMYl!f, Yl!f, npO':!b - HeamepnelfS. 6) HaCnW>K,t?, (11CKI1.) 4acrn a flUWb rnacHble A, H, E nepeA H 11 HH e cTpaAaTenbHblX np114acn1Hx 11 onnaronbHblX np11naraTenbHb1x a,H e OT rnaronos Ha - aTb (·RTb) OT rnaronos Ha - 11Tb (- eTb) pa3Mewamb - pa3MewaHlfu1u CMOp~umb - CMOp~eHHb/U 3aCeRmb - 3aCeRHHb/U yauaemb - yauaeffi:lb1u CJlOBa) Pa3Ae11MTenbHblii b Pa3Ae11MTe11bHb1ii b 1. nepeA e, e, IO, R 1. nepeA e, e, io, R , - nocne np11cTaBOKHa cornacHyio: 11 He nocne np11cTaBK11: Oii}bf:.3a, iiOcYbtj_M, OiJbB.mb, ll b~T, nb!2, secen b~, Bb)gra, sopo6bl;1 npeffb!2_6Une iiHb/U - - - s cno>KHblX cnosax nocne aavx-, 2. B HeKOTOpblX 11HORJbl4HblX cnosax mpex-, 'lembipex-: OeYXgRPYCHblii nepeA o: 2. B 11HORJbl4HblX cnosax naaun120H, Meaan120H, 6yn120H, - nocne np11CTaBOK a<J-, UH'-, KOH'-, 00-, Cif)-: KOMnaHgOH, 6amangOH UCJp. ~IOmaHm, Wh,eK(4UR, KOHblOHKmypa, DlYheKm, cy6'beKm - nocne nepso~ yacrn cno>KHoro cnosa: qJeflbObeiep& 3anOMHMTb! b He n11weTCR: a) nepeA a, o, y, :i: noaoKOHHUK, cyMemb, C3KOHOMUmb, cazumupoaamb 6) B CllO>KHOCOKpaL.LjeHHblX cnosax: ~cnu b Ha KOH4e M B cepeAMHe LfMCflMTenbHblX b B KOHLe cnosa b B cepeA11He CJlOBa OT 5 AO 20; 30 B 111.n. 11 B.n. CeM~ 1. B KpyrnblX ,qeCS'ITKax OT 50 ,QO 80 mpuHaOL(amg 2. 8 KpymblX COTHS'IX OT 500 ,QO 900 mpuoL(am,g ceMgoecRm, ceM,gcom 3anOMHl1Tb! Her b: nRmHaoL(amb, wecmHaOL(amb, ceMHaoL(amb, aocef'ill:laOL(amb, oeaRmHaoL(amb 1. B OKOH4aHl1HX Cyl..LleCTBl1TellbHblX 11 np1111araTeJlbHblX 1. B KOpHe CJlOBa cee<./illi],l/y>t@lj @ Ka, iiilft10in, sKefiYOb, o'5KifZ (rn.), noo'5KifZ (rn .) 2. B cycpcp11Kcax cyLL1eCTB11TenbHblX 11 np1111ararenbHblX 2. B OKOH4aHl1HX maronos aonl./OK, 3BUl./OHOK, 2pow0ebtii, e>Koebtii ne~ me ..m 3. Ha KOH"e Hape41.uA • ~ ;11. 3. B cycpcfn1Kcax crpa.QarenbHblX npi'14acrvu1 ~ orrnaronbHblX..., .... 2opRl./O, cae>Ko, xopowo np1111ararenbHblX nel./liHbtii, nuwlIHHbtii, aoopy>KlfH 4. B cnosax-11cKn104eH11s:1x: woe, w opox, Kpbt>KOBHUK, KamowoH, WOK, w opmbl, WOMnon, 4. B cycpcp11Kcax maronOB 11 Cyl..LleCTBl1TeJlbHblX, KOTOpble Ma>Kop, woy, U3>Ko2a, o6>Kopa, l./OKambcR, 'lonopHblU, w opHUK, 06pa3osa1111cb or arnx rnaronos 3amywgebiaamb _3amywgeKa eel/op, 0)1(02 (cyll.(.), noo>Ko2 (cyll.(.), mpyll.(o6a, mpell.(omKa 5. B cycpcp11Kcax onnaronbHblX np1111ararenbHblX 11 O,QHOKopeHHblX cyl..l.eCTs11renbHblX Yl./eHbJii - Yl./e6a, myw Hblii - mywi°HKa 6e3 y,QapeHHH B cydlcp
  • 49.
    0, E, Enocne ~ e pa3HblX 1.1acn1x pe1.1P.1 0 1. no.Q y,QapeHHeM: nanbmet@ nut@ ffc)Kcifib, nep40eb1t1 2. B HeKOTOpblX HHOR3bl4HblX cnoeax 6e3 y,QapeHHR nana4yo 0 (.QBOpe1..1), CKepjJO(My3. nbeCa B 6blCTpOM TeMne) 3. li1CKJllOYeHHe: !JOKOmyxa 111 1. B KOpHe cy1..4ecTeHTeilbHb1x: 4UPK; LiiiHiJR 2. B cnoeax Ha - LIHR: aKa4uR, unn10MuHa4u>1 1!1CKJllOYeHHR: Ljb/ZaH, Ha Ljbtn04Kax, LjbtnneHOK, 4bl4, Ljb/KHymb CJlMTHO pa3AeJlbHO COI03bl MecTOHMeHHR c YaCTHl..IBMH 1-1 npe,QnoraMH, HapeYHR 4T06bl 4TO 6bl Mbt 04eHb moponunucb, fl OyMan, 4ffio 6bl MHe 13bt6pamb ~ He ono3oamb no4umamb. Ha noe3o. To>Ke=Ta10Ke=1-1 To >Ke fl ~ omobtxan e Kpb1My. fl eb1nonHRn rMo;e 3aoaHue, OH ~ omob1xan 13 KpbtMy. 4mo u mbt. @ oHu omob1xanu e KpbtMy. TaK>Ke=TO>Ke=H TaK >Ke (npuMep ebtwe) fl JI~~ )/(4e oqJOpMun pa6omy, KaK UOH. npw1eM npM '!eM 3KcnepuMeHm 6btn npo13eoeH Mb1 He noHRnu, npu 4~M mym yoa4HO,~ enep13bte. MOR noopyza. npMTOM npM TOM BbtcmynneHue n,Ju mlS;.,, Maza3uHe ecmb cooep)/(amenbHoe u (flpumoM) anme4Hb/U KUOCK uHmepecHoe no c;popMe. 3aTO Ja TO fl eepHyncR no30Ho,<iifjjg13ce n M. Muwa cnpRmancR 3a mo oepeeo ycnen. 111TaK (e 3HaYeHHH BBO,QHOro 111 TaK C Ha~ cnoea «cne,QoeaTenbHO») V1 maK 3aKOH4UnOCb Hawe ~ ece Ha4uHaeM cHa4ana. nymewecm13ue. HapeYHR MecTOHMeHHR c npe,QnoroM 3a'!eM 3a 'leM 3a4eM maK paccmpaueambcR? 3~ 4~M nouoewb, mo u Hauoewb. 3aTeM 3a TeM OH 3aoyMancR, 3ameM 3~· rrl°1eM noeopomoM 6yoem (nomoM) ocmaHOl3uncR. 30aHue meampa. OT'!ero OT '!ero Om4ezo (no4eMy) mbt maKot1 ofh 4~ao OH He Moz omop13amb zpycmHb1t1? Cl3oezo e3znRoa? Orroro OT Toro OH ono3oan, ommozo HUKozo o/ti m~zo noobe3oa ombexana He 13cmpemun. MaWUHa. no'!eMy (nO'IEiM) no '!eMy no4eM ebt maK wyMume? OH He noHRn, ifo ~MY cneoyem zomoeumb ypoK. noTOMy (noceMy) noTOMY OH paooeancR nomoMy, 4mo n Hm~MY nu nymu Mbt eepHeMcR eepHyncR e poOHbte Mecma. OOMOU? no3TOMY no 3TOMY OH He xomen eb1oaeamb n o :JmOMY HanpaeneHUIO moeapu11.4et1, no:JmoMy cneoyem :JneKmpu4Ka. MOn4an. E/E 6eJ y.QapeHHR 3epKBnbl© ilefloeamb, CUmLjeBb/U bl 1. B OKOH48HHH cy1..4eCTBHTeJlbHblX: peCHULfiil.I cmpaHu4i2i] 2. B np1-1rn>1<aTeJlbHblX cycpcj>1-1Kcax nucu4biii (x13ocm), cecmpu4biii 'lepe3 Aect>111c CJlMTHO CnO>KHbre np1-1naraTenbHb1e 1. 06oJHaYaeT oneHKH 1..1eerne: 1.06pa30B8HHble Ha OCHOBe meMHO-CUHUU CJlOBOCOYeTaHHR: cepo-3eneHbtt1 Ol3eHao4amu3ma)l(HblU 2. 06pa30BBHHble OT CJlO>KHblX (oeeHao4amb :Jma)/(et1) cy1..4eCTBHTeJlbHblX, KOTOpble opeeHepyCCKUU (,[1peeHRR Pycb) nHWyTCR yepeJ ,Qecp1-1c: 10zo-3ana0Hb1t1 (10zo-3anao) 3anOMHMTb! TRHb-WaHbCKut1 (TRHb-WaHb) 0611.4ecmeeHHO none3Hbtt1 3. 06pa30BBHHble nyTeM CJlO>KeHHR CJlOB, Me>1q1y KOTOpblMH MO>KHO noCTaBHTb COI03 @: Kucno-cnaoKut1 (KuCnblU u cnaOKUU) 41-1cn1-1TeJlbHoe non (nony) 1. BrnpaR YaCTb cnoea 1. BrnpaR YBCTb cnoea HaYHHaeTCR c n : H84HHaeTCR c comaCHOiii, non-nuMoHa, non-nyKoeu4b1 KpoMe n : 2. BrnpaR YaCTb cnoea nonMempa, nonoecamozo HBYHHaeTCR c macHoiii 6yKBbl: 2. nony-: non-anenbcuHa nonxm.eHu 3. BrnpaR YBCTb cnoea 3. B COCTaee HapeYHiii: RBJlReTCR HMeHeM enonzonoca, enono6opoma co6cTBeHHb1M: non-<1JpaH4uu 3anOMHMTb! 1) PaJ.QenbHo! non- HMeeT caMOCTORTenbHOe 3HaYeH1-1e, OTOpBaHO OT cy1..4eCTBHTeJlbHOro comacoeaHHblM onpe,QeneHHeM: non_cmonoeou_no)l(KU 2) CnHTHo! Cnoeo 4emeepmb e cno>KHblX cnoeax: 4em13epmfibcfJUHan L1epe3 Aect>Mc 1. Cno>1<Hb1e npe,Qnorn: u3-3a, u3-noo 2. CnO>KHble HapeYHR: Mano-noMany, 4ymb-4ymb, m04b-e-m04b 3. 4acrn1..1b1 -mo, -Ka, -Oe, -c, -mKa, -mKo 4. Me>1q10MernR c noernpeH1-1eM ocHoe: ax-ax! ox-ox! 5. npHCTBBKa KOO- H cycj>cj>HKCbl -mo, -fluOO, -Hii6Yab B HapeYHRX H Heonpe,QeneHHblX MeCTOHMeHHRX 6. npHCTaBKH 00-, B'- (w-), B HapeYHRX C cycpcj>HKC8MH -6My, -6iy, -biX, -LJX, -fr 3anOMHMTb! YBCTHl..lbl eeOb. 130("' MOfl, 6b1, u e nHWyTCR pa3AeJlbHO "1H</JopM84ffOHHO- Cnpaao4HaR ra6nHlja © 000 •MH</Jonnacr•, 2004 r. MocKBa, KawupcKoe wocce, 21 E-maJt maif@mfoplastru Htrp:i www.mfoplastru Te · 095 320-94-89 -= f095 320-9'-88 "'00 0 V) "' "'0 r- 0 "'
  • 50.
    05PA30BA-HffE '-' PY66KHH B3blK !..JB.CTb 3HaKM npenMH3HMSIB npOCTOM npeA,nO>KeHMM 3HaK111 npem1HaH111S1 np111 OAHOPOAHblX LlneHax npeAn0>KeH111S1 3ans1TaS1 CTaBl'ITCSI np111Mepb1 1. Ecn111 HeT COI030B. BoT }')Ke non1Hyn111cb no 6eperaM nyra, oropOIJ.bl, nonR, poll.(111. 2. Ecn111 eCTb nosTopS1t0LJ..(111ecs:1 coeA111 H111TenbHb1e 111n111 pa3Aen111TenbHb1e cot03bl 111-111, Aa-Aa, 111n111-111n111, n11160- /11 6eper, 1t1 Mope MOn'lan111. B 3HaKOMOill caKJ1e oraHeK TO Tpenernn, TO cHoaa rac. n11160, He TO - He TO Ill AP - 3. Ecn111 eCTb npornBlllTenbHble COI03bl a, HO, .a.a (=HO) . OH noillMaJI era B3rf1R/J,, HO He OCTaHOB/llJICR. noaop'la/1OH, 11.a He nOCMefl ocnywaTbCR. 4. nepeA BTOpO~ 4aCTblO COI030B: KaK - TaK Ill, He TOnbKO - 3apeao pacnpocTp8H/llJ10Cb He TOJlbKO Ha/J, ~eHTPOM ropo11.a, HO "' 11.aneKO BOKpyr. HO Ill, XOTSI Ill - HO, HaCKOnbKO - HaCTOnbKO Ill AP· 'fepTbl era He TO 'ITO nepenOM/11/1/llCb, a CKPlllB/11/1/llCb /II C/J,BlllHYJllllCb. 5. Me:>KJW BCeMlll OAHOPOAHblMlll 4neHaMlll , OT11.oMa, OT11.epeabea, 111 OT rany6RTH111, 111 OT ranepe111 - OT acero no6e)l(aJ1111 /J.flltlHHbJe KOM6111HlllpOBaHHblMlll 6eCCOI03HblM 111n111 COI03Hb1M cnoco6oM, ecn111 cot03 nosTopeH 6onee OAHOro pa3a. TeH/11. 3ansiTaSI He CTaBlllTCSI np111Mepb1 1. Ecn111 ecTb coeA111H111TenbHbl~ 111n111 pa3Aen111TenbHbl~ 170/J,Ka K8'1HYJ18Cb, nO/J,HRJ18Cb /II /llC'le3f18 . COI03 (111, .a.a(=HO) , 111n111, n11160). 011.Ha>K,11,bl 17e6e/J,b, PaK 11.a l.4yKa ae3rn c noKJ1a>Keill B03 B3Rf1/11Cb. 2. BHYTPlll rpynn OAHOPOAHblX 4neHOB, coe.a.111HeHHblX ,lJ.eT111 co6111pan111 B necy ne'le6Hb1e TpaBbl 111 RrO/J,bl, rp1116b1111 opex111. nonapHo. 3. B 1..1enbHblX Bblpa:>KeHlllSIX: Ill TO Ill ce , Hill CBeT Hill V1BaH HlllKlll(/JOPOB/11'1 6blf1 Hiii )1(/118 Hiii MepTB. 3aps:i, Ill TaK Ill CSIK, Hiii AHeM Hiii H04bl0, Ill AP · T04Ka c 3ansno~ (;) CTaBlllTCSI Me:>K,ll,y pacnpOCTpaHeHHblMlll OAHOPOAHblMlll 4neHaM111 , ecn111 eCTb BHy-TpeHHllle BblAeneHlllSI Me:>K,ll,y HlllMlll: Ha,Qo, 'IT06&1 KOCTep 6&m, BO- nepB&IX, 6e:Jp,&IMeH; BO- BTOP&IX, He O'leH& )1(8POK, a B- TpeT&fAX, B nonHOM 6e3BeTplAIA. T111pe CTaBlllTCSI, ecn111 ecTb nponycK npoT111B111TenbHOro cot03a: He B roCTfA - 3a on&ITOM. AeoeTO'l111e CTae111TCS1 1. nocne 0606LJ..(at0LJ..(ero cnosa, nepeA OAHOPOAHb1M111 4neHaM111. 2. Ecn111 nocne 0606LJ..(at0LJ..(ero cnosa CTOSIT cot03bl KaK-TO, a lllMeHHO, TO eCTb, Hanp111Mep, TO nepeA HlllMlll CTaBlllTCSI 3ans:iTaSI, a nocne HlllX - ABOeT04111e. 3. nepeA nepe4111cneH111eM OAHOPOAHblX YneHoB 6e3 0606LJ..(at0LJ..(ero cnosa, B Aenoso~ 111 Hay4HO~ pe4111. T111pe CTaBl/ITCSI 1. nocne OAHOPOAHb1x YneHOB , nepeA 0606LJ..(at0LJ..(111M cnOBOM. 2. nocne OAHOPOAHb1x YneHOB, ecn111 snepe.a.111 y>Ke ecTb 0606LJ..(at0LJ..(ee cnoso (111 .a.soeT04111e), HO npe.a.no>KeH111e He 3a1<aHY111saeTcs:1 3TlllMlll np111Mepb1 H111'1era He 38MeTHO 6blf10 0)1(/llBJIR/Oll.(ero KaprnHy: Hiii OTBOPRBW/llXCR 11.aepeill, Hiii Bb/XO/J,/llBW/llX OTKY/J.8 - H/116y/J,b /1/0/J,eill, H/llK8K/llX )l(/lfBb/X xnonoT /II 3860T /J,OMa. EMy nO/J,888/1/llCb 06bl'IHble B TpaKT/llpax 6JllO/J,8, K8K-TO: ll.(111, M03rlll c rapOWKOM, COC/llCK/11 c KanycTOill. Ha co6paH111111 np111CYTCTBoaan111: c-ry11.eHT&1, acn111paHT&1, npeno11.aaarnn111. np111Mepb1 CTOn, Kpecna, CT}'flbR - ace 6&1no caMora TR)l(enoro 111 6ecnoKoillHora caoillcrna. 8CJO/J,y: BBepxy /II BH/113Y - nen111 )1(8BOPOHK/ll. np111aHaK111 0THOCSITCSI HenocpeACTBeHHO K cyLJ..(eCTBlllTenbHOMy, xapaKTepll13YIOT npeAMeT c O,ll,HO~ CTOpOHbl 111n111 nepe4111CnSllOT pa3HOBlll,ll,HOCTl1 0,ll,HOro npe.a.MeTa. MO:>KHO noCTaBl1Tb COI03 11 . npM3HaxM 0THOCSITCSI TYT 6&1n111 RpKaR ra031J./llKa 111 KpacH&1e, opaH)l(eB&1e 111 )l(enTb1e n111n111111. Hac-rymma 11.o>K,11,J1111BaR, rpR3H8R, TeMH8R oceHb. np111Mepb1 OBaPH noe3,ll yxe.D.BBHO CTOHT y nonyCTaHKa.
  • 51.
    3HaKM npenMH3HMSI npMnpMnO>KeHMSIX 06oco6mnoTcR npMMepbl. 1 . OAlllHO'IHble 11111111 pacnpoCTpaHeHHble YroMneHHbti!t 11.onroi!t pe'lb/O, fl 3aKpbtn rna3a 11 3acHyn. Ho Tbt B3b11-pan, Heo11.on11Mbti!t, 11 cornacosaHHble np11111o:>KeH111R, ec11111 OTHOcsncR K 11111'1HOMY MeCTOlllM€HllllO. CTafl TOHeT KOpa6nei!t. 2. PacnpocTpaHeHHb1e cornacosaHHb1e np11111o:>KeH111R , KOTOpble CTORT noc11e onpeAe11ReMOro '-lacbt, npoao11.11Mbte c Mono11.e:>Kb10, 6btnl1 3apR.£J.KOi!t 6011.pocm Anfl naana. cy~eCTBlllT€11bHOro 3. OAlllHO'IHble cornacosaHHb1e np11111o:>KeH111R, ec11111 CTORT noc11e onpeAe11ReMoro cy~.• ec11111111x 6011bwe Tearp oca>K,llano Mono11.oe Mope, 6yi!tHoe, Hanop11croe. ConHue, aen11KonenHoe 11 OAHOro , B oco6eHHOCT111 ec11111 nepeA cy~. y:>Ke ecTb flPKOe, nO,[J,Hl1Manocb HB,ll MOpeM. onpeAe11eH111e. 4. CornacosaHHoe np11111o:>KeH111e, CTOR~ee snepeA111 onpeAe11ReMoro cy~ecTB111Te11bHOro , c A06aso'IHblM np11Bne'leHHble RPK11M CBeTOM, 6a60'IKl1 np11neTen11 11 Kp}'>Kl1nl1Cb OKOnO </>OHBpfl. o6CTORTe11bCTBeHHblM 3Ha'leHll1€M . BBOAHble C110Ba Ill KOHCTPYKU,111111 Bb1Ae11RIOTCR 3anRTOi:1: KoHe'IHO, He O,QHH EsreHHH CMJITeH&e TaHH BH,QeT& MOr. 81>1, JI BHJKY, nio6HTe npHpO,Qy. He RB11RIOTCR BBOAHblMlll Ill He OTAe11RIOTCR 3anRTblMll1 C110Ba Ill C110BOCO'leTaH111R: BBOC&, 6yKsan&HO, 6y.QTO, s.qo6asoK, B,QOBepweHHe, s.qpyr, B KOHe'IHOM C'leTe, BPJIA nH, sce-TBKH, e,QBB nH, KBK 6y.QTO, KBK 61>1, K TOMY JKe, MeJKAy TeM, no peweHHIO, npH6nH3HTen&HO HAP· 06oco611RIOTCR npMMepbl 1 . ,[J,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1 11111111 HeCK011bKO Aeenp111'1aCTll1i:1 , OTHOCR~lllXCR K OAHOMY ConHue. cnpRraaw11cb 3a y3Koe c113oe o6naKo, 3onornr KpaR ero. rnaro11y. 2 . OA111HO'IHb1e Aeenp1114acrnR (He B 3Ha'leH111111 nowyMeB, peKa ycn0Ko11nacb, BHOBb nerna a 6epera. Hape'l111R). He 06oco611R10TCR npMMepb1 ' 1 . ,lJ,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1, npesparnsw111ecR B ycTOi:1'1111Bb1e o6opoTbl pe'l111 : cnycrn pyKasa,c110MR ro11osy, He nepeBOAR Ab1xaH111R Manb'll1K 6e>Kan cnoMR ronoay {o'leHb 6btCTpo). lllAP· 2 . OAlllHO'IHble Aeenp1114acT111R, 111Me10~111e 3Ha'leH111e flKOB wen He TOpOnflCb (Me,[lneHHO). 0 nporynKe OH paCCKB3btBan CMeflCb (Becena). Hape'l111R. 3. ,lJ,eenp111'1aCTlllR c 3aBlllCll1MblMll1 C110BaMll1 , TeCHO no CMblC11Y C11111Bal0~111eCR c rnaro110M . Crap11K c1111.en onycrna ronoay. 4 . rpynnbl OAHOPOAHblX '111eHOB, COCTOR~llle 1113 Manb'l11K OTBe'lan OTKPOBeHHO 11 H11CKOnbKO He CMyll.jaf/Cb. Hape'llllR 111 Aeenp111'laCrnR . npM OTCYTCTBMM marona - CBR3KM CTBBMTCR TMpe 1 . Ec11111noAne:>Ka~ee111 CKa3yeMoe - cy~ecTB111Te11bHb1e B VIM. n. 2 . noAne:>Ka~ee Ill CKa3yeMOe Bblpa:>KeHbl '1111C11111Te11bHblMll1 B VIM. 11111111 OAlllH 1113 HlllX - '1111C11111Te11bHOe, BTOpoi:1 - cy~eCTBll1Te11bHOe B VIM.n. KH11ra - 11cTO'IH11K 3HaH11i!t. nf/Tb/O BOC8Mb - COPOK. ,[ln11Ha 80nrl1 - 3688 Kl1nOMeTpOB. >K11Tb - po11.11He cn}'>Kl1Tb. 4 .0AlllH 1113 rnaBHblX 'IJleHOB npeAflO:>KeHlllR Bblpa:>KeH lllH<)>lllHlllTlllBOM, a Apyroi:1 - cy~ecTBlllTenbHblM B VIM . n . np0113BO,[J,11Tb 3<f><f>eKT - 11X Hacna>K,[leHl18. T111pe He CTaBlllTCR, ec11111 nepeA CKa3yeMblM CTOlllT OTp111u,aH111e HE 11111111 cpaBHlllTeJlbHble COI03bl : KBK, TO'tHO, KBK 6yATO M AP·: npy.Q KBK 6neCTJIU(ee 3epKano. Cep.Q14e He KBMeH&. Ec11111 nOAfle:>Ka~lllM RBJlReTCR 11111'1HOe MeCTOl11MeH111e, TO Tlllpe , KaK npas111110, He CTaBlllTCR: OH CKenTHKH MBTepHBnHCT. VICKJ1IO'l€Hllle: np111 nOA'lepKHYTOi:1 3Ha'lll1TeJ1 bHOCTll1 BblCKa3blBaHll151, ec11111 Ha M€CT0- 111M€Hllle 111 3Ha 'le H111e nC!MleT 11or111'lecKoe yAape H111e : OH - sawa PBAOCT&, sawa cnasa! Ec11111 n e pe.a CKB3ye MblM CTOIH CJ10Ba B OT, 3 --/Ji ITT 3TO TO rnpe CTaBITTCSI n EPEJJ. 3Tlll Ill : T041HOCTJ. If tcpaTJCOCTJ. - SOT nepswe AOCTO#HCTBB npo3b1. MH¢tOpMaLl.MOHHO- cnpaao'iH8A Ta6nM~ © 000 •lllH<l><>nnacT-, 2006 r. Moc<sa, KawMpc1<oe wocce. 21 E-mail mai@inloplasLru: Http/ c ...... c
  • 52.
    06PA30BAHHE ~ 6GKMM A3blK 3HaKM npenMH8HMSIB cnO>KHOM npeA,nO>Ke MM. 3ansnasi He CTaBlllTCSI: 1. Me:>t<Ay npeAflOJKeHlMlMlll, coeA111HeHHb1M111 COYlllHlllTenbHblM 111n111 pa3Aen111TenbHblM COI03aMlll, ecn111 lllMelOT 0614111~ BTOpOCTeneHHbl~ YneH 111n111 0614ee np111AaTOYHOe npeAflOJKeH111e. 3ansiTaSI CTaBlllTCSI: 1. Me:>t<Ay npoCTblMlll npeAflOJKeH111siM111,sxoAS1l4lllM111 s COCTaB cnOJKHOCOYl!IHeHHOro. TO"IKa c 3anSITOM CTaBlllTCSI: 1. Ecn111 coeA111HsieMb1e npeAflOJKeH111si 3HaY111TenbHO pacnpocTpaHeHbl, 111Me10T BHYTPlll ce6si 3anS1Tb1e 111n111 MeHeeTeCHO cssi3aHb1 Me:>KAY co6o~ no CMb1cny. T111pe cTae111Tcsi: 1. Bo BTOPOM npeAflOlKeHllllll COAeplKlllTCSI HeOJKlllAaHHoe np111coeA111HeH111e 111n111 pe3Koe npoT111sonocTasneH111e. 0TAensieTcsi 3ansiToit: 1. np111AaTOYHOe npeAflOlKeH111e OT rnaBHOro. Ecn111 OHO CTOlllT BHYTPlll rnaBHOro, TO c ABYX CTOPOH. 2. np111AaTOYHble npeAflOlKeHlllSI C COCTaBHblMlll COI03aMlll nOTOMY 'ITO, BMeCTO Toro 'IT06bl, nocne Toro KaK 111 AP· (np111YeM 3ansiTasi cTaBlllTCSI n11160 nepeA BCeM COCTaBHblM COI030M, n11160 nepeA 'ITO, 'IT06bl1 KaK, B 3aBlllClllMOCTlll OT lllHTOHau,111111 Ill CMblCna). 3anSITOM He OTAensieTCSI: 1. HenonHoe np111AaTOYHoe npeAflOJKeH111e, cocTosi14ee 1113 OAHOro cnosa 111n111 co103a. He pa3AensiioTcsi 3ansiTb1M111: 1. Hepa3nOlKlllMble COYeTaHlllSI: CAenaTb KBK cne,qyeT, CAenaTb KaK nonano, npHXOAHT& KOrAa B3AYMBeTCR, HATH KYAB rna3a rnRART, KpH'l8Tb 'ITO eCTb MO'IH, 6yA& 'ITO 6yAeT Ill AP· 2. CoYeTaHlllH He TOn&KO 'ITO, He TO 'ITO, He HHB'le KaK, TOn&KO 'ITO He, see paBHO 'ITO Ill AP· 1. 06opOTbl , HaY111Ha1014111ecS1 cpaBHlllTenbHblMlll COI03aMlll KBK, 6yATO, cnOBHO, TO'IHO, 'leM, HeJKenH, KBK 6yATO Ill AP· 2. 06opOTbl , HaYlllHa1014111ecsi COYeTaHlllSIMlll KBK ff, KBK npaBHnO, KBK HC/Ul/O'leHHe, KBK scer1ta, KBK HapO'IHO Ill AP-. KPOMe Tex, YTO BXOASIT B COCTaB cKa3yeMoro. np111Mepb1. V13 oKowKa )J,aneKo 6necrnT ropbt 11 BM)J,eH /J,Henp. np111Mepb1. 803)1,YX )J,b/WMT aeceHHMM apoMaTOM "1 BCR np11po)J,a O>KMBflReTCR. np111Mepb1. TaTbRHa, no COBeTY HRHM co611paRCb HO'lb/O BOPO>KMTb, TMXOHbKO npMKa3ana B 6aHe Ha )J,Ba np116opa CTOfl HaKpblTb," HO crnno CTpawHO BAPY• TaTbRHe. np111Mepb1. OH 3HaK no)J,aCT - "1 Bee XOX04YT. np111Mepb1. Kor)J,a COflHl..je nO)J,HMMaeTCR Ha)J, nyraMM, R HeBOflbHO ynb16at0Cb OT pa)J,OCTM. Ha)J, )J,OflMHoilr, r)J,e Mbt exan11, cnycTMflMCb TY4M. - OH He RBMflCR Ha 3aHRTMR, noTOMY 4TO 3a6onen. He XO)J,"1 B arnKy )J,0 TeX nap, noKa He nony4MWb OT MeHR npMKa3a. np111Mepb1. MeHR cnpoc11n11, Ky)J,a R noe)J,y neTOM. fl o6bRCHMn Ky)J,a. np111Mepb1. OH BbtnOflHMn pa6oTY KaK cne)J,yeT. OH np11xo)J,11n KOr,ll,a B3,ll,yMaeTCR 11 yxo)J,11n He npo~aRcb. CecTpa 6b1na MHe ace paBHO 4TO MaTb. 111 neHl!IBO, KaK 6bl 3acb1naH, YAap111n OAlllH pa3 B KOnOTYWKY HOYHO~ CTOPOlK. Bo~Ha 3anOMH111nacb MHe 6onbwe pa6oTo~. YeM yYe6o~. KaK npas111no, s 3Tl!IX Mecrnx 6b1sa10T 06111nbHb1e AO:>t<Alll (cp.:B 3Tlllx MecTax 06111nbHb1e AO:>t<Alll 6b1Ba10T KBK npaBHno ).
  • 53.
    1. Ecm-1 o6opoT1'1MeeT 3Ha4eH1-1e 06cTosne11bcTsa 06pa3a Aei1crn1-1si (11erKo 3aMeHl'1Tb TponffHKa ff3Bffaanacb KaK 3MeR (3Meei'I). Hape41-1eM 1-1111-1 cpopMoi1 Tsop.n .cy11.1.) . 2. np1-1 3Ha4eHl'11'1 OTO)l(AeCTB11eHl'1SI. 0Ha cMoTpena Ha MaTb KaK Ha crapwy10 cecTpy. 3. np1-1 nepeAa4e 3Ha4eHl'1SI "s Ka4eCrne". OH cen 3a pynb KaK wocf;ep. 4. Ec111-1 SIBllSleTCSI CKa3yeMblM 1'1111'1 TeCHO K HeMy npL'1MblKaeT. >K1113Hb KaK nereH,IJ,a. Ha 3KpaHe ace 6b1no KaK a >Klll3Hlll. 5. EC111'1 eCTb OTpl'1L(aHl'1e He 1'1111'1 CllOBa cosepweHHO, nO'ITJ1, spo1te 'TO'lb-B·TO'lb, OH ace ,1J,enaeT He KaK n10,1J,111. Ho'lb/O a ropo,IJ,e 6blflO 1o1MeHHO L'1 AP- caemo no•-1T111 KaK .D.HeM. 6. Ec11L'1 3TO ycToi141'1BOe Bb1pa:>KeHL'1e: 6ne1tH&1if KaK CMepr&, 6necrer& KaK OH 3awen KO MHe 6ne,/],Hb/M KaK CMepTb /II 3epKano, rono1tH&1if KaK co6aKa, seprer&c11 KaK 6enKa s Konece L'1 AP· . MOfl'lafl/llBbliii. 3HaKLll npenLllH3HLllSI B 6eccol03HOM CJlO>KHOM npeAJlO>KeHMH.r~~.~•• 3anRT8SI CT8Bl'ITCSI: np111Mepb1. 1. EC111'1 npeAJ10:>KeHL'1SI o603Ha4atoT OAHOBpeMeHHO 1-1111-1 noc11eAOBaTellbHO Me:>KAy co6oi1, Kparrn . .llaneKO 3a .lloHOM rpOM03,IJ,/llfl/llCb TR>Keflb/e TY'llll, pe3an111 He6o MOflH/11/11, 'IYTb Cflb/WHO rpOMb1xan rpoM. TO'"IK8 c 3anRTOH CT8BMTCSI: 1. EC111'1 npeAJ10:>KeHL'1SI MeHee CBSl3aHbl no CMblCllY L'1 6011ee pacnpocTpaHeHbl (oco6eHHO ec11L'1 BHyrp1-1 HL'1X eCTb 3anS1Tble). BpeMR CTO/llT e~e paHHee, wecmiii 'lac B Ha'lane; 30JlOT/llCTbliii yrpeHHllliii TYM8H BbeTCfl Ha,IJ, npocenKOM, e,1J,Ba nponycKaR TOflbKO 'ITO noKa3aaweecR conH4e; Tpaaa 6necT111T. AeoeTO'"IMe CTae111Tcsi: np111Mepb1. 1. Ec111'1 BTopoe npeAJ10:>KeHL'1e AOno11H51eT nepsoe. Haaepxy>Kypaan111Hb1iii Kp111K: nT1114b1 ynera10T Ha 10r. 2. Ec111'1 BTopoe npeAJ10:>KeHL'1e pacKpb1saeT coAep:>KaHL'1e nepsoro, nosicHsieT ero 1'1111'1 KaKOi1-Hl'16YAb ero 411eH. Cmnb aeceno necTpeeT 4aeTaMw RpKo >KenmeT.D.POK, CKPOMHO ClllHelOT KOflOKOflb'l/llK/11, 6eneeT 4enb/M/ll 3apocnRM/ll naxy'laR poMawKa. 3. Ec111-1 BTopoe npeAJ10:>KeH1-1e yKa3blsaeT npi-t4"1HY Toro, o 4eM rosop1'1TCSI s nepsoM. 8,!J,pyr fl 'IYBCTBylO: KTO-TO 6epeT MeHR 38 nne'le /II TOnKaeT. I J~-~~r~ -i.-ir-~=·- . - • :_ II.- f"."!:• TL11pe Me>K,ly noA11e>KaW.L11M Lil cKa3yeMblM.~.. T111pe cTae111Tcsi: np111Mepb1. 1. EC111'1 npeAJ10:>KeHl'1SI pl'1CYIOT 6blCTpyto CMeHy co6b1rni1 "111"1 npocHyncR - nRTb CTaH4/llM y6e>Kano H83a,IJ,. Cblp BbJnan - c H/llM 6blfl8 HeO:>K1'1AaHHbli1 pe3yllbTaT Aei1CTB"1SI. nnyrOBKa TaKOBa. 2. Ec11i-t B npeAJ10:>KeHL'1SIX COAep:>Ki-tTCSI npornsonocTas11eHi-te. Bab/Cb a3neraeT CoKon - >KMeTCR Y>K K3eMne. 3. Ec11i-t nepsoe o6o3Ha4aeT speMsi i-t11i-t yc11osl'1e Aei1cTBl'1SI, o f1ec py6RT - ~enK/11 nernT. Ha3aancR rpy3,IJ,eM none3ai'I a KY30B. KOTOPOM rosopl'1TCSI BO BTOPOM. 4. EC111'1 TO, 0 4eM rosopl'1TCSI B nepBOM npeAJ10:>KeH"11'1, cpaBH"1BaeTCSI Mona111T cnoao - conoaei'I noeT. c TeM, 4TO CKa3aHo s APYrOM . 5. Bropoe npeAJlO:>KeHi-te 3aKJlto4aeT s ce6e pe3y11brar Aei1crni-tsi s ConH4e .D.blMHoe acraeT - 6y,1J,eT ,1J,eHb ropR'lllliii. nepBOM, BblBOA "13 Hero. 1. Ecn111 cnoea aeTopa CTOSIT nepeA npsiMOH pe'"lblO: 1. To noc11e HL'1X CTaBL'1TCSI ABOeT04"1e. BanR, Tenno o6HRB 3a nne'l/11 MaTb, ycn0Ka111aana ee:''Tbl He TpeBO>KbCR, MaMa ". 2. Ecn111 npsiMasi pe'"lb CTOMT nepeA cnoeaM111 aeTopa: 1. To noc11e Hee CTaBi-tTCSI 3ansiTasi .,, T1-1pe. "fl m6R H/llKOMY He BbJ,IJ,aM",- mp>KecrneHHO o6e~ana OnR. 2. EC11"1 B npSIMOi1 pe4"1 COAeP:>K"1TCSI sonpoc "111"1 BOCKJ1"1L(aHi-te, TO nocne CTaBi-tTCSI sonpOC"1TeflbHbli1 "1Jl"1 BOCKJ11'1L(aTeflbHbli1 3HaK.,, Ti-tpe. "KTO 3TO 6bln?" -He,IJ,OyMeHHO no,IJ,yMan OH. 3. Ecn111 cnoea aeTopa H8XOARTCR e cepeAMHe npsiMOH pe'-1111: 3.a) EC11"1 Ha Mecre pa3pb1Ba AOll)l(Hbl 6blJ1"1 CTOS!Tb He T04Ka, sonpOC"1TeflbHbli1 3HaK "111"1 BOCKJ11'1L(8TeflbHbli13HaK"1, TO CJlOBa aBTOpa Bb1AellSllOTCSI c o6ei-tx CTOpOH 3anS1TblM"1.,, rnpe. "fl saw OP/J.lllHaTOp - cero,1J,HR ,1J,e>Kyp10". 3.6) EC11"1 Ha MeCTe pa3pb1Ba AOJl:>KHa 6blfla CTOS!Tb T04Ka, TO nepeA CllOBaM"1 aBTOpa CTaBL'1TCSI 3ansiTasi .,, rnpe, a nocne - T04Ka L'1 rnpe. Brnpasi 4aCTb npsiMoi1 pe4i-t - c 6011bwoi1 6yKBbl. 'Taoe nplllCYTCTB/lle 3,IJ,eCb Heo6XO,IJ,/llMO, - CKa3ana OHa. - np111e3>Kaiii". 3.B) EC11"1 Ha MeCTe pa3pb1BaAOfl:>KeH CTOS!Tb sonpOC"1TellbHbli1 "111"1BOCKJ11'1L(8TeJ1bHbli13HaK, TO nepeA CllOBaMi-t asrnpa CTaBi-tTCSI 3TOT 3HaK.,, rnpe, a noc11e • T04Ka L'1 rnpe. Brnpasi 4aCTb npSIMOi1 pe41'1 - C 6ollbWOi1 6yKBbl. ''no'leMy BBOCeMb?- cnpoc111na OHa. - Mara3/11Hbl 38Kpb!B810TCR KweCT/11". l/IH<jlOpM34110HHO· cnpaeO'lHa11 rn6n1143 © 000 « lllHcponnacr", 2007 r. r. MOCKBa, Kaw~pcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru
  • 54.
    OliPA30BAHHE CnMCOK HeK0Topb1x Hape'"IMMM H Bblpa>KeHMM. B6nll131!1 BneperoHKl!l 6e3 B8AOMa 6e3 cnpocy B60K BnepeMe:>KKY 6e3 Orn5lAKl!1 6e3 TOnKy no ABOe B6pOA (OT 6e3 OTKa3a 6e3 YMOnKy nOA KOHeu,nepeMe>KaTbCR) BB8K 6e3 npocBern 6e3 ycrnn111 nOA MblWKaMl!lBnepeMeWKY 6e3 pa36opy 6oK o 6oKBBepx (OT nOA Mb1WKl!1 BBblCb nepeMew111BaTb) (B3f1Tb) Brny6b Bnono6opoTa 3a rpaH111u,eVI 3aOAHO nOAP5lA BAaneKe BnOnOBl!IHY 3a rpaH111u,y 3anaH1116parn noA c111ny BAanl!1 Bnopy(no 3aMY:>K 3a nonHO'-lb nOA CTaTb BAanb MepKe) 3aMY:>K8M nOA Y3AU,bl BABOe B nopy (BO Ha aBOCbBpeMR) BA06aBOK Ha 6ery HanoKa3 C B8AOMaBnocneACTBl!11!1 BAOfOHKY BnOTbMaX HaBeK HanonOBl!1HY cBepxy AOHll13YBApe6e3rn HaB8Kl!1 (c,D.enaTb) BnpaBAY c MaxyB 3aKnl048Hl!18 HaBepx Ha nonnYT111 BnpaBe CMOnOAYB3aMeH Ha B3rn5lA HanononaM BnpoK c HaneryBKOH8LJ, HaB3Hl!14b Ha nopyKl!1 BnpocaK HanpoKaT CHl!13Y AOBepxyB KOHLJ,8 Ha Bl!IAB npOTl!1BOB8C KOHLJ,OB Ha Bl!1AY Hanpo4b Bpa3 B KOpHe Bpa36111BKY HaBp5lA n111 HapaBHe BKPYTYIO HaBCTpe4y HapacnawKy Bpa3pe3 BKyne HaBblT5l:>KKY Ha peAKOCTb BM1!1r Bpacnnox Ha pblC5lX AO KpaVIHOCTl!l BpaCCblnHylO Ha rna3 AOBHaV!Mbl Ha CKaKy BPOA8 Ha rna3oK Hey3HaBaeMOCTl!1 BHaKl!1AKY HaronoBy Ha cnaBy AOHl!13YBpyKOnawHyt0 B HaCM8WKY BP5lA n111 (pa36111Tb) HaCMepTb BHa'-lane Ha A111BO ( 611tTbCR) BHl/13 B cepAu.ax Ha AH5lX Ha CMepTb BCneA Ha Abl6bl (111,ll.Tlll)BHl!14bl0 B o6pe3 Bcnenyt0 Ha CMex Ha3aBTpa B o6w,eM Bcnyx HaCT8:>Kb Ha3no BOB8K B CTap1!1HY Ha3y6oK HayraA BOB8Kl!1 BCTapb HaKaHyHe HayAa'-ly BTaVIHe (CK838Tb) BOBP8M5l(B (xpaH11tTb) Ha neTy Ha XOAY HY:>KHblVI '-lac) BTP111AOpora Han1!1LJ,O Ha U,blnO'-IKax Bo Bceopy:>Kl!11!1 B XOAY Ha M111r Ha'-leKy B OAl!1H04KY B u,enoM Ha HeT Ha41!1CTOTY BO 1!136e:>KaHl!18 BW1!1pb Ha OTnl!14HO Ha5lBY BOl!1CTl!1HY B WYTKY HaOTMaWb H8B3Ha4aill Boo6w,e Bb5lBb Ha ow,ynb HenoAaneKy B OTKpblTYIO Hanepe6oill He noA c111ny BnepBble HaneperoHKl!1 He nOA CTaTb HanepeKop nOA'-laC nOA4111CTYIO no3aB4epa noHeBone nOOAl!1H04Ke no naM5lTl!1 no npaBy nocepeA111He no cTap111HKe nOYTPY cnne'-la (py611tTb) c pa3roHa c pa3Maxy CP5lAY CXOAY Cbl3HOBa 4epec4yp AO OTKa3a AO CBl!1AaHl!15l AOma
  • 55.
    A6c~111cca anennS1~111S1 aKKI11t1MaT1113a~111S1 annapaT aKKOMnaHeMeHTannaCClllOHaTa aKKOMnaH111posaTb anneHA1t1~111T aKKOPA anneTlllT aKKYMYnSITOP annn111Ka~111S1 aKKypaTHblill apT111nnep111S1 annerop111S1 ac111MMeTp111S1 anneS1 accaM6neS1 ann111raTop ann111Tepa~111S1 anrnop aMMlllaK aHHOTa~lllSI aHHyn111posaTb aHT8HHa 6ann .(eA1t1H111~a 0~8HK111) 6annMa 6annacT 6annoH 6aJ1110WlpoBaTbC51 6apOKKO 6app111KaAa raMMa reHepan111cc111Myc rn66oH rnnnonoTaM aCCll1CT8HT accoHaHc accopT111MeHT acco~111a~111S1 anecTaT anpaK~1110H acpcpeKT 6acceil1H 6a~111nna 6enneTp111crnKa 6ecCOHHll1~a 6111cceKTp111ca 6occ 6p111nn111aHT HO: 6p1t1nbSIHT) 6t0nneTeHb BQ)t()f(l/1 B03)t()f(8HHblil1 Bbl)t()f(8HHbl111 rpaMM rpaMM8Tll1Ka rp111nn rpoccMeillcrnp rpynna rynanepYa A111Crnnn111posaHHb1!:1 All'l<PQ>epeH~anbHbl~ All'l<Pct>Y3111SI AOn11ap ,QpeCCll'lpoBaHHbli:1 111All'lnllll'ISI ll'IJ1Jll0311'1SI ll'IJlJllOMll'IHa~ll'ISI ll'IJlJllOCTpa~ll'ISI 111Mnpecc1110Hlll3M ll'IMMYHll'IT8T IllHAlll<l><i>epeHTHblH Ka11n111rpacp111S1 Kan111n11S1p Kacca Kacca~111S1 KacceTa K8CCOH KJ18CCll1~1113M KJ18MM8 Konnera Ko11ner11rn KOJ1n8KTll'IB KOJ1n8KTOp KOJ1J18K~ll1SI KOJlOHHa KOJlOCC (sen111KaH) KOMlllCCap KOMll1CCll1SI KOMM8HTap11111! Macca Macca)K M8CCll'IB MeTann Met.tt.to-conpaHo ceCCll'ISI cenep c111n11a6111yecK111il1 Cll'IMM8Tpll1SI ll'IHT8J1J18KT lllHTeJlJllllreHUlllSI 111nnOAPOM 111ppat.tlllOHaJlbHblH 111pp111ra~111S1 ll'ICKYCCTBO KOMMYHll13M KOMMYTaTop KOMMIOHll1K8 KOMnpecc KOMnpeccop KOMnpOMlllCC KOHrpecc KOH~8CCll1SI Kopann KOpp8KTHblil1 KOppeKTOp KOppecnOHA8HT KOpp03111SI Koppyn~111S1 KOTT8p)K K03cpcp111~1t18HT Kp111crnn11 Kp111craJ111w1ecK111H Kpocc KpOCCBOPA n1116peno MlllnJlll'IOH MlllCCll'ISI MO)t()f(888nbHll'IK MOnnlOCK MOHOrpaMMa MYCCOH Hose11na onno3111~111S1 onnoHeHT CT8J1Jla:>K CTpemOKOKK cy66orn na11a~~o naHHO napaJ111e11orpaMM napa11ne11b nacca)K nacca)K111p naccaT naccaT1t1)K1t1 naCClllBHblill Perpecc pe:>K111ccep TenerpaMMa T8HHll1C Teppaca Teppll'IKOH neppoH neCCll1Mll13M npecc npecca nporpaMMa nporpecc nponen11ep npocpecc111S1 Tpacca Tp11111n1t10H Tponneil16yc Tpynna ~ennt0no3a wocce sn111rpaMMa 3CC8H~ll1SI scpcpeKT © 000 «111Hcjlonnacr», 2008 r . MocKsa, Kaw1-1pcKOe wocce, 21 E-mail: mail@infoplast.ru Http://www.infoplast.ru Ten ./cjJaKc: (499) 940-93-23 Ill I4 607061 651873
  • 56.
    06PA30BAHHE ~ PYGGKHH Sl3blK 0CHOBHble cxeMblpaa6opa B pycCKOM Sl3b1Ke. 1. CAenaTb TpaHcKp111rn..1,111io, nocTas111s YAapeH111e. 2. Pa36111Tb cnoso Ha cnorn. 3. OxapaKTep1113osaTb cnorn: a) YAapHbriil/ 6e3yAapHbriil; 6) 3aKpblTbliil/ OTKpblTbliil; 4. OnpeAen111Tb Kon1114ecrno 6yKB 111 3BYKOB, ycTaHOBlllTb COOTBeTCTBllle Me:>K,D,y HlllMlll . 5. OxapaKTep1113osaTb rnaCHb1e 111 cornacHbre 3syK111: a) rnacHbJiil : YAaPHOCTb/ 6e3yAaPHOCTb; 6) cornaCHbliil : rnyxoiil/ 3BOHK111ii1 ; rnepAbliil/ MS'lrKllliil. Mop<t>eMHblH paa6op. 1. Ha3BaTb 4aCTb pe4111 (1113MeHs:ieMas:i 111n111 Helll3MeHs:ieMas:i). 2. 8b1Aen111Tb OKOH4aH111e Ill OCHOBy. 3. noA60pOM POACTBeHHblX cnos BblAenlllTb KOpeHb cnosa. 4. noA60pOM cnos c OAlllHaKOBOiil CTpyKTypoiil BblAenlllTb np111crnsKy 111 cy¢¢111Kc. YcTaHOBlllTb 111x ¢YHKL.J,llllll B cnose. 5. lpa¢1114ecK111 BblAen111Tb see MopcpeMbl s cnose 111 CAenaTb BblBOA 0 ero COCTaBe. Mop<1>onon·1'~ecKl1H pa36op. rnarona. 1. Ha4anbHas:i ¢opMa (111H¢111H111rns) . 2. nocTos:iHHbre np1113HaK111: a) BlllA (cosepweHHbriil 111n111 HecosepweHHbriil); 6) B03BpaTHOCTb; B) nepeXOAHOCTb; r) rnn cnps:i>KeH111s:1. 3. HenocTOs:!HHble np1113HaK111: a) HaKnoHeH111e; 6) 4111cno; s) speMs:i (ecn111 ecTb) ; r) n111L.J,o (ecn111 ecTb); A) POA (ecn111 eCTb) . 4. cDyHKL.J,llls:l B npeMO>KeHllllll. npM'laCTJ1R. 1. Ha4anbHas:i ¢opMa (111MeH111T. naA. eA. 4111cna My>K. poAa) . 2. nocTos:iHHbre np1113HaK111: a) BlllA; 6) 3anor (AeiilcTBlllTenbHbliil 111n111 cTpaAaTenbHbriil); s) speMs:i. 3. HenocTos:iHHbre np1113HaK111 : a) nonHoe 111n111 KpaTKoe; 6) POA; s) 4111cno; r) naAe>K. 4.cDyHKL.J,llls:l B npeMO>KeHllllll. P,eenpM'laCTMR. 1. Ha4anbHas:i ¢opMa (111H¢111H111T111B rnarona) . 2. BlllA. 3. cDyHKL.J,llls:l B npeMO>KeHllllll. Hape'IMR. 1. Pa3ps:1A no 3Ha4eH11110. 2. CrnneHb cpasHeH111s:1 (ecn111 ecTb) . 3. cDyHKL.J,llls:l B npeMO>KeHllllll. Cnoeoo6pa3oeaTenbHblH pa36op. 1. YCTaHOBlllTb npOlll3BOAs:!W,YIO OCHOBY, 2. 8b1Aen111Tb cnosoo6pa3osarnnbHb1e a¢¢111Kcb1. 3. Ha3BaTb cnoco6 06pa3osaH111s:1 AaHHOro cnosa. YKa3aTb npoL.J,eccbr, conposo:>K,D,aiow,111e cnosoo6pa3osaH111e. Mop<1>onorw~ecKl1H paa6op. HMeHM cyu.iecTBMTen&Horo. 1. Ha4anbHas:i ¢opMa: 111MeH. naAe)J( eA. 4111cna. 2. nocTos:iHHbre np1113HaK111 : 1. Co6crneHHoe 111n111 HaP.1111.J,aTenbHoe. 2. 0AywesneHHoe 111n111 HeoAywesneHHOe. 3. KoHKpeTHOe,oTsne4eHHOe, co6111paTenbHOe, sew,eCTBeHHOe. 4. PoA: My>KcKoii1, >KeHcK111ii1, cpeAH111ii1. 5. T111n CKnOHeH111s:1. 3. HenocTos:iHHbre np1113HaK111: a) 4111cno; 6) naAe>K. 4. cDyHL.J,llls:! B npeMO)J(eHllllll . HMeHM npMnaraTen&Horo. 1. Ha4anbHas:i ¢opMa ( 111MeH. naA. eA.4. MY>K. poAa). 2. nocTos:iHHbre np1113HaK111: a) pa3ps:1A no 3Ha4eH11110 (Ka4ecrneHHoe, OTHOClllTenbHOe, nplllTs:l>KaTenbHOe); 6) y Ka4eCTBeHHbrx: nonHas:i 111n111 KpaTKas:i ¢opMa; B) y Ka4eCTBeHHblX: CTeneHb cpasHeHllls:l (nono)J(111TenbHas:1, cpasH111TenbHas:1, npesocxOAHas:i). 3. HenocTOs:!HHbre np1113HaK111: a) POA; 6) 4111cno; s) naAe>K. 4. cDyHKL.J,llls:l B npeMO>KeHllllll. HMeHM 'IMCnMTen&Horo. 1. Ha4anbHas:i ¢opMa (111MeH. naA.). 2. nocTOs:!HHble npi113HaKlll : a) neKClllKO-rpaMMaT1114eCKlllii1 pa3ps:!A (Kon1114ecrneHHoe, nops:iAKosoe, co6111parnnbHoe, AP06Hoe); 6) no CTpyKType (npocTOe, cnO>KHOe, COCTaBHOe); B) oco6eHHOCTlll CKnOHeHllls:l. 3. HenocTOs:!HHbre np1113HaK111: a) naAe>K; 6) POA (ecn111 eCTb); s) 4111cno (ecn111 ecTb). 4. cDyHKL.J,llls:l B npeMO>KeHllllll. MecTOMMeHMR. 1. Ha4anbHas:i ¢opMa (111MeH. naA. eA. 4111cna) . 2. nocTOs:IHHble npi113HaKlll: a) pa3ps:!A no 3Ha4eH111io; 6) oco6eHHOCTlll CKnOHeHllls:l. 3. HenocTos:iHHble np1113HaK111: a) naAe>K; 6) 4111cno (ecn111 ecTb); s) POA (ecn111 ecTb).
  • 57.
    CnYJKe6HblX 'lacTeil pe'IM. 'lacnw,&1. 1.paaps:iA no 3HaYeH11110. npe1tJ10ra. 1. Henpo111aBOAHb1"111111111 npo1113BOAHb1"1. 2. 8b1pa)f(aeMoe 111M OTHOWeH111e. 3. C KaK111M naAe)f(OM ynoTpe611eH? Co103a. 1. npOCTOif111111111 COCTaBHOif1. 2. CoY111H111TellbHb1"111111111 noAYll1H111Te11bHb1"1. 3. CoeA111Hs:ieT Y11eHb1 npeAJ10)f(eH111s:i 11111111 YacT111 CllO)f(HOro npeAJ10)l(eH111s:i . 4. 8b1pa)f(aeMble 111M OTHOWeHll1Sl. MeJK.QoMeTHR. 1. nepBll14HOe 11111111 npOll13BOAHOe (B TOM 4111Clle COCTaBHOe). 2. nepeAaBaeMble 111M 3MOU,1110HallbHblif1 OTTeHOK, no6~eH111e. Cnosoco'leTaHHR. 1. 8b1Ae11111Tb CllOBOCO'ieTaH111e 1113 npeAJ10)f(eHll1Sl . 2. YKaaaTb HaYanbHYIO ¢opMy. 3. 8b1Aellll1Tb rnaBHOe (3HaKOM x ) 111 3aBll1Cll1MOe CllOBa (yKa3aTb CTpellKOill) . 4. OnpeAe11111Tb T111n no xapaKTepy rnasHoro c11osa (rnaro11bHOe, 111MeHHoe, HapeYHoe) . 5. OnpeAe11111Tb rnn css:ia111 (cornacosaH111e, ynpas11eH111e, np111Mb1KaH111e) . 6. YKaaaTb rpaMMaT111YecK111e cpeACTBa css:i3111 c11os (oKOHYaH111e, npeAflor) . 7. OnpeAe11111Tb xapaKTep CMblCllOBblX OTHOWeH111"1 Me)f(Ay c11osaM111 (onpeAe11111TellbHb1e, 06beKTHb1e, o6CTOSlTellbCTBeHHble) . npoCTOrO. OnpeAe11111Tb rnn npeAJ10)f(eH111s:i : 1. no U,ellll1 BblCKa3blBaHll1Sl (noseCTBOBaTellbHOe, no6yA111TellbHOe, sonpoc111TellbHoe) . 2. no 3MOU,1110HaJlbHOif1 OKpaCKe (BOCKJ1111U,aTellbHOe, HeBOCKJ1111U,aTellbHOe) . 3. no CTPYKTYpe : a) no COCTaBY rnaBHblX 'illeHOB (ABYCOCTaBHOe, OAHOCOCTaBHOe) ; yKa3aTb Tll1n OAHOCOCTaBHOro npeAJ10)f(eHll1Sl (onpeAe11eHHo-11111YHOe, HeonpeAe11eHHo-11111YHOe, o6o6~eHH0-111114HOe , 6e3111114HOe, Ha3blBHOe) ; cnoco6 Bb1p~eH111s:i rnasHoro YlleHa; 6) no HaJ11114111IO 11111111 OTCYTCTBll1IO BTOpOCTeneHHblX YlleHoB (pacnpocTpaHeHHOe 11111111 HepacnpocTpaHeHHoe); B) no nOllHOTe COCTaBa (nOllHOe 11111111 HenOllHOe) ; yKa3aTb npony~eHHble 411eHb1 ; r) OCllO)f(HeHHOe 11111111 HeOCllO)f(HeHHOe (06pa~eH111eM , BBOAHblMll1 CllOBaM111 , OAHOPOAHblMll1 , 06oco611eHHb1M111 Y11eHaM111 , cpaBHll1T8llbHblM o6opOTOM) . 4. 06bSlCHll1Tb nocTaHOBKY 3HaKOB npen111HaHll1Sl. CnoJKHoro. 1. Bb1Ae11111Tb ero YaCTll1 , OTMeTll1Tb 111X rpaHll1U,bl. 2. noKa3aTb rpaMMaTll14eCKll1e OCHOBbl B Ka)f(AOif1 YaCTll1. CnoJKHoco'IHHeHHoro. 1. OnpeAellll1Tb cpeACTBa c111HTaKc111YecKoill css:i3111 : Ha3BaTb COI03, yKa3aTb ero Tll1n no 3HaYeHll1IO (coeA111H111Te11bHb1"1 , nporns111TellbHb1"1) , no CTPYKTYPe (OA111H04Hblill, napHblill) , no cpyHKU,111111 (OA111H04Hblill , nosrnps:i10~111illcs:i) . 2. 06bSlCHll1Tb nocTaHOBKY 3HaKOB npen111HaHll1Sl . 3. Cocrns111Tb cxeMy. CnoJKHonop,'IHHeHHoro. 1. YKaaaTb rnasHoe 111 np111AaTOYHoe. 2. Ha3BaTb, YTO nos:icHs:ieT np111AaTOYHoe: rnasHoe npeAJ10)f(eH111e B u,ellOM 11111111 OTAellbHOe ero CllOBO (yKa 3aTb YaCTb pe4111 3TOro CllOBa). 3. 0TMeTll1Tb, Ha KaKoill sonpoc OTBeYaeT np111AaTOYHas:i YaCTb 111 KaKOBO cpeACTBO Cll1HTaKC1114eCKOll1 CBSl3111 (COI03, COI03HOe CllOBO). 4. OnpeAe11111Tb T111n npocToro npeAJ10)f(eH111s:i (onpeAe11111TellbHOe; 1113bSlCHll1TellbHOe; o6CTOSlTellbCTBeHHOe: MeCTa, speMeHll1 , CTeneHll1 111 o6paaa AeillcTs111s:i , np111Y111Hb1, u,e11111 , ycTYnK111 , yc11os111s:i , c11eACTB111s:i ; cpasH111Te11bHoe ; np111coeA111H111Te11bHOe, conocTas111Te11bHoe). 5. 06bSlCHll1Tb paccTaHOBKY 3HaKOB npen111HaH111Sl . 6. CocTas111Tb cxeMy. 6ecco103Horo cnoJKHoro. 1. OnpeAellll1Tb CMblCllOBble OTHOWeHll1Sl Me)f(Ay YaCTSlM ll1 (OAHOBpeMeHHOCTb, nOClleAOBaTellbHOCTb, npll14111HHO- ClleACTBeHHble OTHOWeHll1Sl , yc11os111e 111 AP -). 2. YKaaaTb rpaMMaT111YecK111e cpeACTBa, Bb1p~a10~111e OTHOWeHll1Sl Me)f(Ay YaCTSlMll1 (111HTOHaU,111Sl , nopSlAOK ClleAOBaHll1Sl YaCTeill 111 Ap .) . 3. 06bSlCHll1Tb paCCTaHOBKY 3HaKOB npen111HaH111Sl . 4. CocTas111Tb cxeMy. npeltf10JKeHHR C npRMOH pe'l&IO. 1. HaasaTb c11osa asrnpa 111 nps:iMylO pe'ib. 2. OnpeAe11111Tb 111x pacno11o)f(eH111e no OTHoweH11110 APYr K Apyry. 3. 06bSlCHll1Tb paCCTaHOBKY 3HaKOB npen111HaHll1Sl. 4. CocrnBll1Tb cxeMy. 5. Paao6paTb OTAellbHO KaK npeAJ10)f(eH111s:i c11osa asTopa 111 nps:iMy10 pe'ib. © 000 «VlHcponnacT», 2007 r. r. MocKsa, Kaw111pcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru 0 00 00
  • 58.
    0 S PA 3 0 B A H 111 E HH.!!!9_nlACT 100 ~'!> CMCTEMA MEP MBECOBto;,'VOll -·EAMHMl.lbl, AOnycKaeMble K npMMeHeHMIO OcHOBHbie eAMHMl.lb• HaMMeHoeaHMe Ha11MeHoeaH11e 06o3Ha'leH11e HapaeHe c eAMHM4aMM Cl/I: Be/lM'IMHbl Merp - eAlllH1114a AJllllHbl K111norpaMM - eAlllH1114a MaCCbl ,l1m1Ha ceKYHAa - eAlllH1114a BpBMBHlll Macea aMnep - eA111H1114a Clllflbl 3flBKTp1114BCKOro TOKa BpeMR MOnb - BAlllH1114a Ko111114ecrna Bel1jecrna Cima 3neKrpw1ecKoro TOKa KaHAena - eA111H1114a c11111b1 csera TeMneparypa ,QonO/lHMTe/lbHble eAMHMl.lbl C111na csera paAt11aH - SA111H1114a nnocKoro yrna crepf1A111aH - eAlllH1114a TSflSCHOro yrna npOM3BOAHble eAMHM4bl npocTpaHcTea M epeMeHM HaMMeHoeaHMe HaMMeHoeaHMe 0603H3'1BHMB ee/lM'IMHbl PyccKoe Me>KAYHap. nno114aAb KBaApaTHblH MSTp M2 m2 06b8M Ky611148CKlllH MSTp M3 m3 CKopocib MSTp B ~SKYHAY MIC mis YcKopeHue M8Tp Ha CBKYHAY MIC2 ml s2 B KBaApaTe '-lacrora nep110A.npo4ecca rep4 r1.1 f;lz '-lacrora apa114eH11R CSKYHAa B MlllHYC c-1 s- 1 nepeoi.1 CTeneH111 YrnoaaR CKOPOCTb paAlllaH B CSKYHAY paAfc rad/s Yrnoaoe ycKopeH11e paAlllaH Ha CSKYHAY paAfc2 radls2 B KBaAPaTe nepUOA CSKYHAa c s npoM3BOAHble eAMHM4bl MexaHM'teCKMX eenM'IMH nnoTHOCTb KlllJlOrpaMM Ha Kr/M3 kglm3 Ky611148CKlll~ MSTp YAenbHblH 06bBM Ky611148CKlllH M8Tp M31Kr m31kg Ha KlllJlOrpaMM 11MnynbC KlllflOrpaMM-MeTp Kr•MIC kg•mls (KOflff'iBCTBO AB11JKBH11fl) B CBKYHAY Cuna, aec HblOTOH H N YABnbHb/H aec HblOTOH Ha HIM3 Nlm3 Ky611148CKlllio1 MSTp !laaneH11e nacKaflb na Pa Pa6ora, 3HeprnR A>KOYflb A>t< J M01l4HOCTb BaTT BT w noaepXOCTHOB HaTRJK8Hl18 HblOTOH Ha MeTp HIM Nim /111HaMl1'1BCKaR BR3KOCTb nacKaflb-CBKYHAa na·c Pa·s K11HeMarn4ecKaR KBaApaTHbli.1 MeTp M2/C m2/s Bfl3KOCTb B CBKYHAY npoM3BOAHble eAMHM4bl TennOBblX eenM'IMH Konu'lecrao rennOTbl A>KOYflb A>t< J YAenbHOB Kon-ao A>KOYflb A>KIKr Jlkg rennorb1, YASnbHblB rennOTbl nnaeneH11fl, napoo6pa3oeaH11fl, cropaH11R ronnuea YAenbHaR rennoeMKOCTb TeMneparypHbli.1 S'lpKOCTb CTlllJlb6 anocrn11b6 0CBBL1jBHHOCTb cj>OT Ha KlllflOrpaMM A>KOYflb Ha KlllflOrpaMM-KSJlbBlllH KSJlbBlllH B MlllHYC c6 ac6 cp HaMMeHoeaHMe 06o3Ha'leHMe MHo>K11re11b npMCT3BKM pyc. MBJKA. 3KCa 3 E 1018 nera n p 1015 repa T T 1012 rnra r G 109 Mera M M 106 Kl1nO K k 1a3 reKro r h 1a2 ABKa Aa da 101 ABLJl1 A d 10-• caHrn c c 10-2 Ml1nnH M m 10-3 MVIK{XJ o~ 0-g sb 1'104 Kp/M2 asb ~0,323 Kp/M2 ph 1•104 flK HaMMeHoeaHMe MHO>KMTem1 KBlllHHlflfllllOH KBaAPlllflfllllOH TplllflfllllOH MlllflfllllapA MlllflfllllOH TblCR4a CTO AeGRTb OAHa COTB.R OAHa AOCRTB.R eAMHMl.lbl PyccKoe MeJKAyHap. 3eyKoaoe AaaneH111e nacKanb MeTp M m na Pa KlllJlOrpaMM Kr kg CBKYHAa c s aMnep A A KBJlbBlllH K K KaHASfla KA cd MOJlb MOJlb mol Macea TOHHa T BpeMR MlllHYTB MlllH min 4ac 4 h CyTKlll CYT d nnocK11i1 yron rpaAyc, 0 MlllHyTa, CBKYHAa paA111aH PaA rad reKTap ra ha f1111Tp fl I KOSrjxf!114eHT nepsoi.1 cTeneH111 npoM3BOAHble eAMHM4bl 3neKTPM'leCKMX .. MarHMTHblX eenM'IMH HaMMeHoeaHMe HaMMeHoeaHMe ee/lM'lMHbl nnOTHOCTb aMnep Ha sneKTp11'1BCKOro TOKa KB. MSTP Kon-so sneKrp114ecraa, KyflOH 3nBKTp11'1BCKl1H 3apflA noaepXHOCTHaR nnOTHOCTb KynoH Ha ::in. 3aPRAa KB. MBTP 3n. HanpRJKBHl1B, BOJlbT ::in. nOTBHljl1an, pa3HOCTb ::in. nOTBHljl1anOB, 31/C HanpflJKBHHOCTb ::in. nonR 0011bT Ha MeTp 3neKTPl1'1BCKafl BMKOCTb cpapaA A6con10THafl cpapaA Ha MeTp A113neKrp114ecKaR npOHl1ljaBMOCTb, 3n. noCTORHHaR 3neKTp11'1BCKOB OM conporneneHue YAenbHOe Sn. OM-MSTp conporneneH11e 3n. npOBOA11MOCTb ClllMSHC MarHvtTHbli.1 noroK se6ep 11HAYKTHBHOCTb reHp111 MarHl1THMI 11HAYKLJ11fl Teena A6con10rHaR MarHl1THaR reHp111 Ha MeTp npoH114aeMOCTb, MafHUTHaR noCTOflHHafl A>KOYflb n p 10-12 cp f 10-15 ano a a 10-18 EAMHM4a AJlMHbl 06o3Ha'leHMe SAMHM4b1 M11Kp0M8Tp HaHOMBTp aHfCTpeM pyc. Me>KA· MKM µm HM nm A A 0603H3'l8HMe PyccKoe MeJKAyHap. NM2 Nm2 Kn c Kn/M2 Clm2 B v BIM V/m <t> F <t>IM Flm OM n OM•M n•m CM s 86 Wb r H T T r /M Him OAHa KBlllHT111111110HHaR MHOlKMTB/lb 10-5 M 10-9 M 10- 10 M f111KOMBTP nM pm 10-12 M 11KC-BA11Hl1lja lllKC-BA. x 1 , 00206·10-1 3 ~ 10-13 M cpM Im 1 (cpeMTOMeTp) = 10-15 M Ceeroeoii roA - paccTORH111e, npoxOAMMOe cseTOBblM ny40M B Te4eHMe OA- Horo rap.a. napceK - paccTORHl<S C KOTOporo P<JAMYC Op6MTbl 3eM/1M BMABH nOA yrnoM, pas bl OP,HoH ce " AB.
  • 59.
    TeMneparypa L./enbCl1R, rpa,qycoc oc pa3HOCTb reMneparyp LjenbCVIR HaMMeHoe. EAMHM4a 3Ha<1eHMe eenM'IMHbl H8MMeHOB8HMe o6o3Ha'leHMe a eAMHM48X Cl1 pyccKoe Me>KA. AflV!Ha aHrcrpeM A A 1·10- 10 VIKC-9AVIHV14a VIKC-0A x 1 00206·10- 13 M caHrnMerp CM cm 1:10- 2 M Ka6enbTOB K6 185,2 M acTpOHOMVIY0CKaR a.e. 1,496•1011 M 8,Qk:lt:Hdl,a CB9TOBOi.i rDA CB. rOA l.y. 9,4605•1015 M napceK nK pc 3,086•1016 M nnollja,qb KBa,qpaTHbli.i CM2 cm2 1•10-4 M2 i;attik:ltia~IIJ ap a a 100 M2 reKrap ra ha 1•104 M2 Ql:i:t!!lM ts~011~~Q~l1~ QM3 Q[]3 l•l Q-6 M3 caHrnMerp nvirp n 1·10-3 M3 Macca rpaMM g 1·10- 3 Kr arOMHaR BAV1Hvi4a a.e.M. u 1,6605·10- 27 Kr MaCCbl (yrnepOAHaR WKana) 2•10-4 KrKaQaT M0TQ1114eCKll1~ Ka(2 ct 4eHTHep 4 g 100 Kr TOHHa T t 1000 Kr 61J~fii18 ta:U:ll:l;!Ia Mldtl rnio 60 ~ YaC y h 3600 c CyrKVI cyr d 86400 c nnoCKVli.i yron C9KYHAa =4,85·10- 6 pa,q MVIHyra =2,91-10- 4 P3A rpa,qyc =0,0175 P3A 0(.l8MC~ ;![CD l 5Z llaA nonHbli.i yron 06 6,28 pa,q (o6opor) JlVIH9i.1HaR caHrnMeTp B CSK CMiC cmi s 1·10- 2 Mi C Cls:CIJCCib ~li:HJCMBIIJ a :tac ~M& ~[!]/b Q 2ZB !.!I~ y3en (MOpCKOi.i) y3 kn =0,514 Mi C KVlnOMere B CSK KMiC kmis 1000 MiC n111Hea'.1H08 caHTYIM0Tp Ha CMi c2 cmi s2 Mo-2 Mi c2 ~CKOpeHvie CeK~HAY B KBa,qpare 4acrora o6opor e CBKYHAY o6ic 1 c 1 Bpallj9HVIR o6oeor e MviH~T~ 06iM 1/60 c-1=0,0167 c- 1 nnoTHOCTb reaMM Ha KZ'.6VIYBCKV1i.i r/CM~ 9ism~ 1•1 o~ KriM~ caHrnMerp Cvina 8VIHa 8VIH dZ'.n 1·10- 5 H MexaH•YeCKoe KvinorpaMM-cvina Krc/MM2 kgf/mm2 =9,81 ·106 na HanpR)!(9HVl0 Ha KB. M'1nn'1M9TP AaeneHvie A•Ha Ha KBa,qpaTHbli.i AVIHiCM2 dyni cm2 0,1 na caHrnMerp T8XHW-18CKa~ am at =9,81-104 na aTMOCcpepa KrcicM2 kgf/cm2K'1norpaMM-C'1na Ha =9,81-104 na KB. CaHTVIM9Tp cpV13VIY9CKaR amM atm 101 325 na (HOpManbHaR) aTMOCcpepa M'1nnviMeTp BOARHOro MM BOA.CT. mmH20 =9,81 na CTOn6a t.a1i:iam:n.1eIP IJI~Il:iQCQ Mt.a IJI CI [!][!] Clg =l33 3 Da cron6a 6ap 6ap bar 1·105 1la Pa6ora, 3pr 3pr erg 1-10-7 A)!( 3HeprviR san-Yac BPY W·h 3600~ K1o1nosarT-Yac KBPY kW•h 3,6•10 A)!( CTapb1e pyccKMe eAMHM4bl 111 111x nepeeoA e eAMHM4bl Cl-1 1 a.e. (acrpOHOMVIYeCKBR 0AVIHV14a) = 1,496•1011 M 1 CB. rDA (cBeTOBoi.i roA) = 9,463•1015 M 1 nK (napceK) = 3,086•1016 M = 3,26 ceeroeoro roAa HeK0Topb1e APeBHepyccKMe Mepbl AecJtTMHa (Mapa 3eMenbHoi.i nnol!13A") - 0 ,9 ra. Kynb (Mapa CbmyYvix ren) - AllR p>t<vi - 151 ,5 Kr, Anl1 ceca - 100,3 Kr. JloKOTb (Mepa AnVIHbl, paeHaR AnviHe noKreeoi.i Kocrn) - 45,5-47,5 CM . CalKeHb KOCaJt {Mepa AnV!Hbl, paeHaR paccroRHVllO or nanb4ee neeoi.i Horn AO KOH4a nanb4ee npaeoi.i pyKvi, BblTRHyroi.i no A"aroHanvi) - 216 vinvi 248 CM. CalKeHb npocTaJI (Mapa AnVIHbl, paeHaR pa3Maxy pyK or KOH4oe nanb4ee OAHOi.i PYKVI AO KOH40B nanb4ee APYrD) - 152 vinvi 176 CM. EAMHM4bl AfllllHbl M11nR MopcKaR MVlnR Ka6enbroe S'lp,q <llyr At0i.1M 5onbWaR nVIHVIR ManBJI nMHMR EAl<IHM4bf CKOpocTM 1,609 KM 1,852 KM (TOYHO) 185,2 (TOYHO) 914,4 MM (TOYHO) 304,8 MM (TOYHO) 25,4 MM (TOYHO) 2,54 MM (TOYHO) =2.12 MM <llyT B C0KYHAY =-0.30 C M'1rui a Yac = 1,609 KM. Y:ren 1,852 (MOPC'<lll' Kll" e ac =O 5 c EAMHM4bl nno1J48AM AKp =4046,9 M2 Kea,qpaTHbl~ APA =0 ,836 M2 Kea,qpaTHbl~ cjJyr =929 CM2 KBBAPBTHbl~ AtOi.iM =645,2 MM2 K ea,qpaTHal1 nVIHVIR =6 ,45 MM2 (6onbWaR) EAl<IHM4bf 118CCbl ToHHa (An"HHBJI • =1 ,01 6 T TOHHa (KopoTKBJI ,.Q,907 T l.leHTMep HHb6i) =50.8 l.le+m<e!J ( KOOOT!OOI) "'45.4 Kr =453.6 r 373,2 r 3n0KTPOBOnbT KMnorpaMM-C'1na- -Merp 3B Krc·M eV kgf•m =1,602·10- 19 A>t< =9,81 A)!( Ha11MeHoe. eenM'IMHbl MOUJHOCTb noeepxocTHoe HaTR)!(8H'1e MoMeHr C'1nb1 il1HTeHC'1BHOCTb B03Ayxa KonMYecreo rennoTbl EAMHM4'1 H8MM8HOB8HMe o603Ha~eHMe 3H8'19HM8 e BAMH114ax Cl/I nowa,q'1HaR cvina KMnorpaMM-C'1na- M0TP B CSKYHAY AMHa Ha caHTMMerp A'1Ha-caHrnMerp K'1norpaMM-C'1na- 3pr e ceKYHAY Ha KB. CBHT'1M0Tp 3pr pyccKOB MBlKA· 3eric ergis n.c. KrC•M/C AMHiCM AVIH•CM KrC•M 3pri c•cM2 3pr Kan kgf·mi s dyn/cm dyn·cm kgf·m =736 BT =9,81 BT Mo-3 Him HO H·m =9,81 H·m erg/c•cm2 1•10-3 Br/M2 erg 1.10 A)!( Kanop'1R KVlnOKanOp'1R KKan cal =4,19A)!( kcal =4,19·103 A)!( YAenbHaH Kanop"" Ha rpaMM Kan/r cal/g =4,19·103 A>KiKr rennora nnaeneHHH, wenbHaH rennora napoo6pa30BaHVIH, YABnbHaH rennora K"1JlOKa11op111H Ha K'1norpaMM 3pr Ha rpaMM KKaniKr 3pr/r kcal/kg ergig cropaHt1R tonm10a YAenbHbl~ pacxoA ronnviea YAenbHa" rennoeM KOCTb seuiecrna rpaMM Ha nowa,q. r/n.c.•Y =3,78·10- 12 Kr//1>1< CMny B YaC 3pr Ha 3pr/r•°C ergi g•°C =1·10- 4 A)!(fKr•K rpaMM-'P3AYCl.lenbCVIH Kanoe•si Ha Kanir•°C cal/g•°C =4,19•103 tJt</Kr•K c11111a toKa Kon1o1Yecreo 3neKTp'1Y8CTBa 3AC. pa3HOCTb noreH4'1anoe, 3n. HanpR>KSHM0 HanpR)!(SHHOCTb 3n0KTP'1Y9CKOro 3n0KTp11Y9CKOe conpOTlllBJl0Hlo10 rpaMM-rP3AYC l.lenbCVIR KHJ10KAn0PHR H8 KKahlKP c KVlnorpaMM-rP3AYCl.lenbCVIH 8All1Hl114a Cll1hbl TOKa Ci c eA. 3apRAa ere BA. 3.a .c. CIC; 8A'1HV14a pa3HOCTVI noreH4vianoe CIC; SA. HanpR)!(8H'1ll ere SA. HanpR)!(SHHOCT'1 ere 3n. SMKOCTVI CM cm 0A. 3n. COnpOrnBnBH'1R CIC ==3,33•10 19 Kh =3,33·10- 1°Kn =300 B =3•104 Bi M 8,99•1011 OM= =9·1011 OM YAenbHOe 3n0KTpVIY9CK00 conporll1BileR111e 3neKTPMY9CKaR npOBOAMMOCTb OM - KB. 0 M•MM2 /M O•mm2 i m MMnnMM9Tp Ha MeTp eA.YA.3n.conp. CIC eA. 3n. npos. ere 1•10=o OM·M 8,99·109 OM·M= ==9•1Ug OM•M YAenbHaR 3Jl9KTpV!Y0CK~ HPOBOAAMOCTb MarHVITHbli.i MarHVITHaR @AYkll~R HanpR>t<0HHOCTb MaFHIATHOfO hbhs:i 3neKTp'1Y9CKall 3HeprMR SA. YA· 3n. npoe. ere 0A. MarH. noTOKa ere MKC Mx SA. MarH . MHAYK4MM l e Gs c1 c raycc) SA. Hanp. Marn. non" 3 Oe Cl C (3pcteA) 3pr 3pr erg Ho-0 Bo 1·10- 4 T =79,6 AIM EAMHM4b106beMa, eMeCT'1MOCT'1 EAMHM4bl AflMHbl Ky6viYeCKBR n'1HVIR =16,4 MM3 TOYKa 0 ,254 MM nviHVIR 2,54 MM Ky6VIY0CKVI~ AIOi.iM = 16,4 CM3 At0~M 25,4 MM BepwoK 44,4 MM Ky6VIY0CKM~ eepwOK =87,7 CM3 <llyT 304,8 MM ApWVIH =71 ,1 CM WrocjJ (1 / 10 BSAPB) =1,23 n Ca)K0Hb =213,4 CM lapHe4 3 ,28 n BepcTa = 500 Ca)!(0HRM=1500 apWVIHBM=1066,8 M BeApO =12,3 n Ky6VIY0CKV1i.i QJYT =28,3 AM3 4erneprb 0 ,21 M3 (AnR CblnYYMX Ten) 4ernepviK Ky6viY. apwviH Ky6viY. YH4MR ApaxMa (AHrnMR) lpaH EAl<IHM4bl o6'bE!M8, BMecTMllOCTM =28,35 r =1,77 r =64,8 Mr TOHHB perncrpOBBJI =2 ,8M3 Ky6'140CKMM l1PA =-0.76 M3 Ky611Y0CK"1M ¢ YT =28,3 AM3 Ky6Vl4ecKMi1 A!Ot<M =1 6 ,4 cM3 5 yuiellb (AHm"") c=36,4 n 5ywem. CWA) >=35.2 n r~ < ..... =4 5 11 r aI1110t< cyxciM CWA) =4 4 n il-1'a ( =568.3 EAMHM4bl MSCCbl AonR =44.4 Mr <llyHT=96 30n. =409,5 r 3onOTHVIK =4 ,27 r nyA=40 cpyHTBM=16,4 Kr nor = 12,8 r 5epKoee4 =163,8 Kr CyxaR nVIHTa (CWA) :>KMAKOCTHBR nVIHTa (CWA) lannoH )!(MAKOCTHbl~ (CWA) 5appenb H0QJTRHO~ (CWA) "1H<PoPMB!jMOHHO-CnpaB04HBR ra611H4a ~ 000 ""111¢onnacr•, 2004 r. MocKBa. KB111HpcKOe wocce, 21 =550,6 Mn =473,2 Mn =3,8 n =159 n 00 00 "'0
  • 60.
    0 6 PA 3 0 B A H 111 E I0 IIOHllTHll: MeXaH H"l:feCKOe JJ;BIDKefUt:e; MaxpocKorurqecKoe Teno; MeXaJlHYeCKOe COCTO.SJ.HH e; MaTepHa.JlbHaJI. TQl.IKa; CHCTeMbT OTcqeTa (mrnp1.P-1am.HLie .li HeHHepuHam.Hl.le); 00 833HMO,ll,ei1CTBHe; BH.llhl .n;s11JKemu1; octtosHhJe MexattHqecKHe serrHqfili&I l Tipnnunm.i: .Ua.JThHO,n;eHcTBH11; cynepn03lfl.IHH; OTHOCHTeJihHOCTH; CHMMeTplrn; 0 ~ coxpaJ1eH111r 3aKOHbI lib IOTOHa 3aKOHbl ,llJJll CHJJ: BCeMHpHoro T.slrOTeHH.Sl; ynpyrncrn; cyxoro " >KH.IlKOro TpeHHl! 3aKOHbI coxpaneH1111: 3HeprHH; HMII)'JThCa; MOMenrn KMDylThca l Oc110&11b1e x apat<TepucTHKH: - noCTynaTeJl.bttoro ,u;BH)J{eHJU1; - spaw,aTenbHOfO .[{BH)l(eHHJI; - KOJ1e6aTeJJhHOro ,llBH>KeHHJI 06b11cne11ue HBJJenuii npupo,11b1 u TeXHul<H: paseoeeCHSI Ten, HeBeCOMOCTH, IlO,ll.'beMHO.H CliJihl KphIIla CaMOJieTa, peaKTHBHOro ,llBH>KeHHJ! H .np. HcnOJlb30oaaue KOne6 aTe.JJbHOro u spa111aTeJJbHOro ,llBmKeHHH B TeXHHKe H 33eanne Ilpupo.na B38HMO- <l>opMyna ,11m1 3aBHCHiIOCTb CHJl bl CHJIbl ,11eiiCTBHH pac'leTa cnJJbI OT paCCTOHHJUI HJJH OT HOCHTeJlbHOii CKOpOCTH CK11a rp3BHT81.11'10HH8• F =G mM .Slem1e-rcst cpyHJ<L~HeH TUOTeHHJI paCCTOllHHll Me)l(lly T R2 B3lll!MO)leiicTByrO!l111MH TeJ13MH Cuna 311e1CTpOMarHHTH3R Fx =-kx .Slsm1eTCS1 cpym<UHeli y npyroCTn paCClOllHHJI (JaBHCllT OT 11ecpopMa1.1>rn) Cm1a TPe!ilUI 3neKYpOM3rHHTHaJI Frp = µN .HaID!eTCJI cpyHIQU!eii a) cyxoro CKOpOCTH OTHOCHTeJTh- 6) lKH)IKOrQ FconP = av,,.,, Horo ABIDKeHJ.Ul VOTH FconP =13v!,. rpacp111Kll1 AB111>KeHll1M 'fro 113yqae'I'? Cpe,11cTBa OIIHCaHIDI MeX3Hli"tleCKOe ll.BHJKeHMe; CHCTeMbl OTcqera; Koop.nHHarn, aepeMell(eHRe; CKOpOCTh, ycKopeH11e; aepHOll, 4RCTOTa; 3MTIJTllyYll3, cpa3a; yTJTOBru! CKOpOCTb; yrnosoe ycKopeHHe; UHKJlll"!eCKall qacTOTa 3aKOHbl ,llBH>KeHHll: P a1moycKopeHHo e C nep eMeRHbIM y cKop eHHeM PaBHOMepsoe .llBH)l{eHHe no OKPY>KHOCTll v= const, x = x0 + vxt l ii= const Vx =Vox+axt 2 axt x=xo +Voxt+2 'lncn ennb1e MeTO/lbl pacqeTS a = ~ = 4n2v2R = 4n2R UC R T 2 ~ K p HBOJI11n eiiHoe Bpall(aTeJJ:&Hoe Kone6aTeJJhHOe y CKOpeHHOe ,llBH>KeH>!e no OKpylKROCTll PasHOMepHoe spam;eHHe BpaileH11e c ycKope11neM rap MOID!qecKHe KOJ1e68HH• Q=-vuUCTUK { CO= cp' v=coR { E = C0 1 =cp11 a=ER { a =-co2 x Xx= XM COS(COf +<p) HerapMOHH"leCKlle Ko11e6aID1• qncnennb1e MeTO/lbl p acqeTS 3aBHCHT JJH cuna CoxpanaeT JJH cun a csoe OT M3CCbl B38H- Kat< aanpasn e- 3H&'lenne np11 nepexo11e KaKOBb1 yCJioBHH npuM eH H MOCTH MO/leHCTBYIOUIHX HS CHJ18 HJ 0,ll,HOii HHepu;naJibHOii ct>op•iyJibI TeJJ cncreMbl B 11pyry10 IlpllMO nponop- B 11onb np51MOJ.:i, CoxpaHsieT, TaK KaK MaTepH811bHh1e T01.fKH KJlH c<j>epK4e- qBOHaJibHa MaccaM coe.nl!HJ!IO!l1eli paccro• 11He R He CKH CHMMeTpH'CJHbie rnapbI B331£MO/leHCTBy!O- B33KMO.UeHCT- H3MC H.slCTC11 ll.J;HX Te JJ BV!O!l1He Tt"1Ja He Ja sHCHT n poTHBOnOJIO)f(- Coxpam1er, Tax KaK ,[(OCTaTO'fHO MaJiaR eenH4Htta .necpop- HO HanpasneHHJO 11e¢>opMal.1H1r x He M3qlfH X nepeMell(e!ilUI H3MeID1eTC}I qacnu~ apu 11ed>OOM8UHll He JaBHCHT IJpOTHBODOJIO>K- CoxpaHlleT, TaK KaK <l>OPMYJI8 FTP =µN BblOOll.HJieTC• HO u anpasneHHJO M OJcy"Jih OTHOCHTeJI.hHOli nptt6moKeHHo, TaK KaK cHJia cyxoro seKTopa CKOpO- CKOpOCTH VOTH ue TPeHIDI 33Bl1CHT OT CKOpOCTn. CTI1 VOTK H3MeHJleTCR Ilpu >KHAXOM TpeHHH .no onpe11enen- HOH cKopocrH Bb100J1HJ1eTC• cpopMyna FconP= a.VOTH H3aTeM Fcon.P= ~v!rn .PasnoMepnoe .nenlKenne Paenoyc1<opeenoe n BHlKeune Paeuoyc1copeuuoe PaettoMepuoe CKOpOCTb YcKopeHue TiepeMemeHHe «l>opM)'na s v= - t ii =0 s= vt Koop.lHllaTII x =-"o +Vi Vxf _ oL___.f t i5 = i50 + iit ii= V -Vo t a_r - 1)1 --..,- rpactiex BHJJ. p;eHJKettnsr 8 3aKM.HOe eanpasneHHe CKOpOCTH H ycKopemu1 TIOCTOJIHHO JIB ycKOpeHHe: a) DO MO.lYJUO 6) DO HarrpaB- neHHJO <l>opM}'na CKOJ>OCTH <l>opM)'n• .)'CKOpeHHJI t '<l>ol*).u mop.Dllll'TW ~·~~---~! npRMOJIHtteHnoe JlBH:iKettne JlBIDKenue no oKnV'Jllo."uocru no OJlHOH npHMOff []Q,ll npl!MblM yrJIOM J:lpyr ( B OJlHY HJIH rrpo- K,lpyry TH.BOnonO)l(H bJe CTOpQHbt) a) nOCTOJIHHO a) DOCTOHHffO 6) DOCTOJIHHO 6) H3MemierCM v = v0 +at 27tR v= -- T - v-vo u2 4n2 a= - =- - R=a= --- R T2 t =4n2 v2 R X =x0 + V0t + . 2n x=Rsmyt a,11 I ,.,_ - - ,.,- >=Rco-~t- T
  • 61.
    <l>K3K'leCKaJ! MaKpOCKOnH'ieCKOe Teno CHCTeMa MaTepHanbHaJ!TO'll<a OIDlchrnae- CocTOl!HHe noKOJ! .IJ:emKeHHe Moe J1eneITT1e llJill paBHOMepHoro c ycKopeHHeM rrpKMoJIHHeHHoro )lBIDKeHHJI CKcTeMa 11eyx Ten CHCTeMa llBYX MaTepHanbHblX TOtJ:eK CYTb 3aKOHa nocrynHpyCT cymecreoerurne HHep111rnJIDHOii CHCTeMbI OTCqeTa BJaHMo.n.eHcTBHe C11nb1 )leHCTBHJI 11. nponrno- orrpeiienRCT K3MeHe- 11eiicreHJ1 paBHhl no MOllYJIIO. Riie CKOpOCTll, T.e. IlpoTHBOilOJTOllCHbl no Ha- ycKopeHHe rrpaBneHHJO, rrpHJioJKeHbl K (ecm•IF=O , To a=EF v= const) m pa3Hh!M TenaM, O)UIOii rrpH- pO.D;bl ft:.2 =-.F21 CTpKMepb1 .ll.BH'IKeaHe KOCMH- J:(eH>KeHHe nnatteT~ B3aHMo.u.eHCTsHe Ten: Co;m- npoJ1BneHHJ1 qecKoro Kopa6mi na11ettHe Ten sa na H 3eMJIH, 3eMJTH 11 JlyHhI, BllaJIH OT rrpHTRrH- 3eMJTIO, TOpMOJKeHHe aBTOM06HJTR H noeepXHOCTH eaiom11x Ten H pa3roe aBTOM0611- 3eMJTJI, 611JIDJ1p1lHb!X rnapoe J1R fpaHHnbI l1HepUHanbHb!e CHCTeMbJ OTCqCTa npKMettH - MaKpo- 11 MeraMHp MOCTH BIDKCHHe co CKO OCTJIMH, MBOro MCHbID.HMH CKO OCTH ceera C~na , pa60TB, 3Hepr~H <llopMyna rpatJ>e1< Cwra TJ!lKeCTH ~Fr =mg mg "' 0Q. " Pa6oTa CWlhl TJ!)l(eCTH.. ~ .. A=FScosa; F=mg; S=hQ mg =.. a=O; A=mgh 0 ~ :.: IloTeH.llHanbHaJ! 3eeprn.>I mgHf·------ . . =... EP =mghQ. " 0 : h..Q H = KH:ee-r11qecKaJ1 3HeprHll EKL h"3 mv2 Q Q. EK=- =mg(H - h)IQ 2 0 H-+Q 5 IToJTHax 3HeprHll :G... mv2 E=mgh+-=mgH 2 H t Cima yrrpyrncTH r F;f ~2 IQ Fx =-kx... Xi -x ~ =,., Pa6om CHJlbl ynpyroCTH ~f l kxi kx2 X2 •e: ="' A=-zx1-2X2 Xi x J: "= ITOTeHI.HanbHax 3Hepr11.>J EJ ..t; kx.2 ',., Ep=2 : " x, x..: Xi..: Q l<HHCTH'leCKaJ! :meprH.>I= EJ .. mv2 k 2 2"'... " EK =1=2(x, -x, ) x, xe: Xi'2e: ITOJTHaJ! 3aeprHJ1 EJ Q :.: kx2 mv2 kx2Q : " E=-+--=-i " x, x... 2 2 2 Xi Ha'laJJbHble ycnoee11 Onacauue Jl,BH*'.eHHR Raqam,HaJ[ Haq3.TlbffasJ lj>opMYllbI TPaeKTopHll KOOpllHHaTa cxopOCTh Yo=h Y:1 j;~o v=-gt tigt2 y=h-- 2 0 x Yo=h y:~. v= - v0 -gt l~ gt2 y=h-v0 t-- 2 0 x Yo =0 y~g V=V0 -gt 'll~ gt2 y= v0 t--- 2 0 x 0 x Yo =0 y~ v. = v0 cosa :oVo lg v, = v0 sina- gt x= v0 tcosa a t' 0 x y=v0 tsina - L 2 Yo =h ye V, =V0 y~ VO Yo lg Vy =-gt X=V 0( ' :.. v v, 0 x gt2 0 xy=h-y Yo= R1+h y u. =u0 cos a. Vo =0 Yo ~ u, =v0 sina. ,,.,. ... -h ' 'Xo h . 2rc / x = (R3 +h)slilTt I R, a VoVo =8KMlc I u:1I Y: I R1~ 2rc I 0 ,,__ / vx0 x y = (R3 +h)cosTt ' CTaTMKa l13Y"aCT ycJJOBH.>J paBHOBeCJlll TBep.zu,rx Ten BM)l,hl PABHOBECID! YcroiPrneoe Ee3pa3JJH'!HOe ~CPEACTBA OIIl1CAHIDI Mo.n;eJTb Tena s CTaT11Ke - a6coJ1K1Tuo Teep.n;oe Teno. ' ___.... HeycToii'lHBoe ~ Ce11Jb - npenllTCTBHe JI;BIDKeHHJO Terra: rroeepXHoCT&, eepesxa H T..n;. / / PeaKUHH CBll3H - Cl!Jla, .n;eikTBYJOIUaJ! Ha Teno co CTOpOHbl CBJl3H, no HOpMaJTH K aanpaenemno BOJMOJKHoro nepeMe1.11eID1.J1. MoMeHT c11nhi - M=±Fd, r.n;e d - nneqo CHnhi 0 3&KOH Ka1<oea MaTeMaTH'lec - B K8KHX CHC- Tpe6oeaHHJ1 BuyrpeuuHe ff3eecTub1 JIH coxpaueHHJ1 CK:8SI 38IlHCb 38K'OH8 TeMaX OTC'leTa K suemHHM CHJJ&M, BLJHOJIHHCTCH 11eiicTBYKIUIHM Ha 3SKOH CHCTeM}' 3aKOH L,mv = const B coxpaHemrn ll:mo,= OOMI HHepnHanbHblX HMll)'Jl.bCa L,mvY= const L.F = O L.mv, = const JaKOH EK+ Ep = const B coxpatteHID! C'' HReprrHanbHblX ::mepnrn - 2 - +mgh = const l:A=O mv2 kx2 - 2 - +- 2 - = Const 33.KOH L=const B COxpaHeHID! fro=COnst I~ ~.! =0~OMeHra llDlll)= mvr= CHJJbl, 11eiiCTeyK1111ee B CHCTCMeTeJI .J1J06bre KoHcepeaTKBllbie (nOTeHUHaJTbHhle) ~CBJILI TJ!rOTeHHJI CH.Thi ynpyrocra I ;lioiiwJ,m CJlf'l&H uapy- lllCHH_H 38KOHOB coxpaeeuea He-r He-r HeT ITpHinum MHHHM)'Ma noTeH.J.lHanbROii 3HeprnH I Y u lCTQff"qHBQ TO ITOJIQ)f(CHHe Tena, B KOTOpOM ero DOTeH- UJlanb!laJ! :mepmll KMeCT eaHMeHbrnee 3Ha'lemie H3 ecex B03MO)l(Hh!X MH</JopMaljHOHHo-cnpaeO'/Ha• Ta6nHllB © OOO•MHljJoonacr•, 2007 r Moa:Ba. Kam.<pacoe wocce.21
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    06PA30BAHHE MOJTEKY.JUIPHO- Ocuoeu1.1e nou11TH11: KHHETlJIIECKMIC r MaCCa 'laCTHQbl; TEOPIDI (MKT) ----1 peACTBa KOHI!eHTPaQIDI qacnm ; "i~~~~~,-= ! 1-ho H3)"1aCT? ! cpe,!Hllll :lHepnur qacr11u; CeolicTBa CHCTeM, cocTOJllllMX MOJlb; MOllilpHllJI Macca HJ 6om,woro 'IHcna MHKPOCKOITH'leCKHX '13CIH11, xapaKTep HX ,!BIDKeHHJI H OCHOBHhIE IlOJIO)KEHIDI BJaHMOAelicTBHJI MKT ! Bee rena cocTOJIT H3 '!aCTHQ Tm1H'!HL1e l!eneHHll: q3CTHl.U>l H3XO.!l!TCJI B .!1H<l><l>Y3Hll; 6ecnopll,!O'lllOM,XaOTH'leCKOM TennoapOBOl{HOCTb; ABHJKeHHH B.R3KOCTh; qaCTHUbJ BJaHMOAeliCTBYJOT APyT c 6pOYffOBCKOe l{BHJKeHHe APyTOM 1 IIPDMEHEHllJI MKT OObRCHEHME M PAC'IET JIBJieHHH A1t<l><!>YJ1tH, Tennonpoeol{HOCTH, Bll3KOCTH (KeneHHH nepeuoca KO~eHTPaJ:{HH MOneKyn, HMll)'ilbCa 11 3uepnrn Tennosoro ABIDKeHHJI MoneKyn) OE'h51CHEHME M PACqET l!Bne1111li 6poyuoacKoro ABIDKeHHJI, Tennosoro pacrnHpeHHJI HnosepXHoCTHoro uaTllJKeHHJI Ilpo1.1eccb1 CucTeMa KOOPAHHaT p-V p-T l130TepMH'leCKHii p Ti>T1 'LL:T= const Ti I T2>T1 T1 0 v 0 T J.fao6apHbiii '[_'[_p = const P2 P2 P1 P1 0 v 0 T l130XOpHb!ii 'L: p V2 V=const V1 I V2>V1 J V2<Vi 0 v 0 T lJ,HKJl l 'b'L1- 4 I 4 0 v 0 T Ll,HKJJ 2 'Lp~I .,_ 4 ,L 4 0 v 0 T TepMH'lecKHif Koacj>cj>HuueHT none3uoro ,11,eiiCTBHll (KII,Z:O AJUI Kpyroaoro npouecca (uHKJ1a) V-T 't:I T2>T1 0 T v P2 P1 J P2<P1 0 T v Vi V1 Vi>Vi 0 T v~ 0 T 'Ll"-0 2 3 0 T Ocuoeub1e nou11TH11: CpeACTBa r-TEPMO)J;JIHAMHKA OITHCaHHJI .n;aeneHJ1e;o&eM; ! TeMnepazypa; pa60Ta H KOilH'leCTBO TennOThl qTO HJ)"laeT? I - <l>YHKnHH rrpouecca; ! BttyTPeHHJIJI 3HeprHll - CsolicTBa M3KPOTe11 H l!BneHHll, Ij:IyuKUHll COCTOJIHHJI ODHpal!Cb ua o6m:He JaJ<OHbl TepMOAHHaMHKH B paMKax 3AKOHhITEPMO~llllAMUJOI MO,!e!IH " repMOAHHaMwtecKaJI I-ii 3aKOH: !'1U = Q + A' CHCTeMa'' M3MeHeHHe BttyTPeHHeli 3HeprHH TepMOAl!HaMH- ! •1ecKoli CHCTeMbJ paono CYMMe KOnH'lecTBa nepe- AaHHOH TennOTbJ QH pa60TbJ BHeLUELllX CHn !. TllIDl'ffiL1e J1sneuH11: Tennoaoe paeHoeecHe, 2-ii 33KOH: TellJJOCMKOCTh, HesoJMOJKeu npo11ecc, eAHHCTBeHHhlM peJynhTa- H3MeHeEL11e arperaTttoro TOM Koroporo 6bma 6i,1 nepeAa'!a 3HeprnH nyreM COCTOJIHHJI BeIQeCTBa Tennoo6Meua OT xonOAHOro Tena K ropll'leMy ! DPOMEHEHIDI TEPMO.l(RllAMHKH 3HEPfETMKA (80% scex JHeprCTH'!eCKHX Janacos 3eMnH - BttyTPeHElllll 3uepnU1 ronn>rna) OE'h51CHEHME AeiicTBHll TennosbJX MaLUHH (TennoshlX ABHTaTeneii, xonOAHnbHhlX MaLUHH, TennOBhlX HaCOCOB) PAC'IEThl TennoeMKOCTeil H pa31111'lHbIX Tell!IOBhlX npo11eccoa KHHeTW!eCKllJI 3Heprn.11 xaoTH'leCKOro lIOC'fYII3TeJlbHOro .!IBll)l(eHH.11 MOJleKyn KHHeTw1ecKaJ1 11 noTeHqHam.HllJI :rneprH.11 KOJle6aTeJlbHOI'O }UIIDKeHID! MOJleK)'Jl TioTe~aJibHllJI 3HeprH.11, 06ycnoBJieHHaJ1 CHJiaMH MOJleK)'llJlpttoro 83al!MO.!leiiCTBHJI X11MJ.1qecKaJ1 3HeprH.11 (3HeprH.11 BH)'TpllMOneK)'IU!pHOro B33HMO.!leiicTBHJi) MoneK)'Jl 3tteprH.11 3neKTpOHHh!X o6onoqeK aTOMOB II llOHOB 3tteprID1 rpaBl!TaUllOHHOI'O B3311MOl{eiicTBHJI Cnoco6b1 HJMeueum1 euyTpeuueii 3uepruH Tena Terrnonepe,11,aqa IKottseKQHJI I TennonpOBO,l(HOCTb l1.3n)"leHHe
  • 63.
    Hn1eueHHe lbMeueuee lbMeneHHe Mo.~•puu 8blpllll(eHHerpafjlRKR Hueauee MaTeMBTH'lecKoe Iloey'lenue Coeepweuue TennoeMKOCTb Bblp8ll(eHHe o6'beMa KOJIR'lecTRB pa60Tb1 (A) euyrpeuueii Te11meparypb1 (D.U) nepeoro ua'lana 38BHCRMOCTR npouecca npouecca (D.V) TeDJIOTbl (Q) '.)HepntR (6U) <t.n TepMO,l1HH8MRKR p(V) D.T A,nua6aTHbrH pV"=const >O 0 >O <O <O 'L0 A'=l'lU <O 0 <O >O >O 0 v f =const 0 >O 0 >O >O ~R l_LJifaoxopHbrii Q=l'lU 2 0 <O 0 <O <O 0 v >O >O >O 0 0 p~J.faoTepMH'!ecKHii pV=const 00 Q= - A' <O <O <O 0 0 0 v v >O >O >O >O >O .?_R 'l=113o6apHbtii - = const Q=l'lU +A' T <O <O <O <O <O 2 0 v "1Aea11bHblM ra3 TepMOA111HaM111YecK11111'1 MeTOA raJ - CHCTeMa MHKpO'!aCTJU~ r83 - M8KpOCKOITH'!eCKall CHCTeMa MO,!J,e.Jlb - TepMo,wrnaM.WieCKall CHCTeMa OcHOBHble ee11111Y111Hb1 Macca Moneicyrrbl m KoHU;eHTJ)llllWI MOJieKyn n Cpe.llHJlll KBa,ll,paTH'IBaJI CKopocTb V Cpe,ll,HJlll KHHeTHqecKaJI 3Heprmi Moneicyn E l.fucno MorreH. V MoJJJ1pHaJ1 Macca M IlocTOJIHHaJI liom.UMaua k 1 _ 2 1 _ 2 2 E- kT p=-nmv =-pv =-n =n 3 3 3 3 U=-vRT 2 IJ,eHTpbl CHMMeTpHH ('IBCTHllbl, 3 3 l'l.U =-vRl'l.T =-8.(pV) 2 2 0CHOBHble Be/1111'ill1Hbl Macca raJa m ~aBJielllie p 06'beM V TeMIIeparypa T IlJIOTHOCTb p BH)'TpeHIDIJI :mepntJI U MoJJJ1pHaJ1 Te[IJloeMKOCTb C YHHBepcanbHaJI raJOBaJI nocTOllHHaJI R m pV=vRT=-RT M OcHOBHble CBOHCTBB IlpHMepbl Ten KJIHCTanna o6pa:Jyiomee peweT1cy) Cunbl B3BHMO.l1eiicTBHll e KJIHCTanne KpRCT8JIJIOB MoneK)'JlllpHb!ii MoneK)'Jlbl Bau-.11ep-Baanbca, .11nnOJib-J1HnOJibHble, HuJKall TeMneparypa nJiaBJieHHll Ha<j>Tanuu BO,l10p0,!1Hble CBll3H HH3Kall TBep.llOCTb MeTaJIJIH'lecKHli IlorroJKHTeJibttble HOHbl 3rreKYpOM8IBHTHhle (MelKJIY 3JieKYpOHHh!M Bb!cOKall Jrrerrrpo- u TenJionpoeoJIHOCTb MeTaJIJibI ra30M " IIOJIOJKHTeJibHhlMH HOHaMH) KoeaneuTHblli ATOMhl HJIH rpynnbl aToMOB KoeaneHTHble CBll3H O<JeHb ewcoKaR TeMnepayYpa rrnaeneHIDl. AnMa3, KpeMHHH 0'1eHb 60JibWall TBep,ll,OCTb 11ouuhlli l1oHLJ (nonoJKHTeJibHble " 3neKYpOMarnHTHbie (MelKJIY HOHaMH) BMCOKall TeMneparypa nnaerreHHR. XpyrrxoCTb IloeapeHHall com. OYpHil8TeJibHble) 0THOClr1Te/1bHas:i B/18>KHOCTb B03AYX8 q>= f 100% Kan1r11111s:ipHOCTb Bb1c0Ta no.llbeMa )l(HJIKOCTH a Kan11JJJUipuoi1 Tpy6Ke h = 2cr cos e pgr TO'lKB pocbl - TeMnepaTypa, np11 KOTOpoil nap nepeXOJl!1T B COCTOllH11e HaCbJLUeH!1ll. noeepXHOCTHOe H8Ts:l>KeH1r1e F I :>i<H.uKOCTb cMa'IHBaeT ue cMa'IHBaeT noeepXHOCTb KailHJIJUlpa t.1H<j>OpM81.1110HHO- cnpaBO~H8ll Ta6n114a ©000 «1'1Hcj>onnacT», 2007 r. r. MocKaa, Kawi-ipcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru N '<I' 0 no,llnucaHO Bnf"laTb 14. 11 2008. T11pilJK 4000 JIG 3aKa3 N• 29242 113,llarenb 000 •l1Hl/JOfJllaCT•, MOCKB<l, KiJwupCKoe wocce, l 1 Ten. (495) 730-01-87. Tunorpaqm• 000 •8..,.,-Crap• 107023, Moc:ICBd, yn 3nenpo3aBOIJO<aff. 20
  • 64.
    0 ~ 06PA30BAHME 3Ml111P111.JECR11iffiA3HC ~ OIIbITbI Kynotta, 3pCTeAa, A~mepa, 0Ma, <llapaAell, MHmrnKetta - HocjJcjJe, MattAenbwTaMa - IlananeKCH TEOPETWIECR11if fiA3HC ~ &ean HJHpOBRHHblH OfrbCKThl : 3neKTPH'leCKHH 3apll.l, 3neKTPl!4eCKOe none, MarHHTHOe aone, eeweCTBO - CHCTCMa 3aplDKeHHblX qaCTifl.I, BJaHMO):eHCTBHe nocpeACTBOM noneii Ocuosuble nonHTHH: q, E, B, C, L, R, E, µ, c 0CHOBHble llJICH: B3afill O.UeiicTBHll, coxpaHe- HHll, OTHOCHTeJ!hHOCTH, 6mf3KOAeiicTBHll ~ Y paeHeHHll MaKceenna. 3neKTPOHHal! TeopIDI KoHCTattTb1: E0, µ0, I c- - ~eoµo .. 3aKOHhl 3neKTPOCTaTH4eCKOro llOJUI 3aKOHbI CTa1.vmHapuoro 3neKTpW1ecKoro DOJUI (aoCTOllHHbfH TOK) 3aKOHbl MarHHTHOro DOJUI 3aKOHbl 3neKTPOMarHHTHOro DOJUI (3aKOH 3neKTPOMarHHTHOH HHLYKl..IHH, aepeMeHHblH TOK) 3neKTPHqecKHe H MarHHTHbie CBOHCTBa BeweCTBa TeopHll 3neKTPOMarHHTHoro aoJUI .. IIPHMEHEHIUI 3neKTPOTex.ID11<a. PaAHoTelCffifKa. 3neKTPOHHXa. 3uepreTHKa .N'!.N'! CxeMa :meKTpH'leCKOH u.enH 3aKOH 0Ma 1 a R b I= Uab 0 CJ 0 R 2 a RJ R2 b I=~ o----e::J----CJ R1 + R2 Rl I=~ 3 ~ R,R22 R, +R2 4 Q e l =- - R +r 5 [I,";':"·'1 ne l= - - R+nr ,1e,r ::e,r e'I I=-- 6 n ......... ...... R-..!:..,1e,r I 'I n R •- a ~C:,r C:-L 0 0 I= - - r 3aKOHbl TOK3 3nerrpITTeCKHe uenu OcuoeH1>1e TeXHH'!ecKHe npHMeHeHHll 3,[( 3neMeHTbJ CTO I3nerrpocT3TH4ecKoe none I MarnHTOCTaTH'lecKoe none MarnHTHb1e OcuoBHLJe HHALI noneil xapaKTepHCTHKH rpaBHTaQHOHHOe 3JJeKTPOCT3TH'leCKOe 06beKTbl B33HMOAeiicTBHll Bee Tena H 'laCTHl..lbl 3apJDKeHHJ>Ie Tena H qaCTH Ubl <llopMynJ>I CHJ!hl F =G m,m2 F=kjq,jjq,j R' r2 HanpllJKeHHOCTb Fg=- - ft E=- m q PaJHOCTb noTeHUHanoe q>, - q>, =g(h, -h,) q>2 -q>1 = E(d2 -d1 ) Pa6oTa no nepeMewelililO A= mg(h, - h,) A= q(q>, -q>,) Tena HJJH 3apl!Aa A=mgh A=qEd Pa6orn no 3aMKHyroil A =O A=O TPaeKTopKH N•N• CxeMa JJICKTpn'lecKoii uenn J aBHCHMOCTb CHJlhl TOK& OT lfftCTOTbl R ~lI 0 c::::J 0 ' (i) 2 0 lie 0 ~t --' (i) L ~1"--3 ~ ' (i) ~~ ~t -4 ' (i) R 5 ~ ~t --- ' (i) R L ~t6 ~ ' (i) L ~t7 ~ - • (!) R L C ~t '"' I 8 ~ ~ (l) =-- '(!) 0 ..fiC O>o ~ ~t 1 9 (l) =-- _,,. 0 ..fiC ro. '(!) /+ I c. CO, = - - c .--ih - .[LC; I 6l 2 o--IH Cil <: Il --0 -~- = 11 ,1L(C1 - C1 )
  • 65.
    IlocrynaTe.llbHoe Bpalll&Te.llbHoe 3JJel<TpOMBrHHTHble llBHll<eHHellBHll<eHHe Be.llH'IHHbl 3JleKTpH'leCKHe DOJl.11 M•ntHTHble noJHI CMe1UeHHe X Yrnoeoe CMe1UeHHe 0. 3ap•.ll q H8HMeHOBBHHe C~opocn x' Yrnoea• cKopocTb 0. 1 CHJJ3 TOK3 q' Toqe1.1Hb1H 33.PAA YcKOpeHHe x" Yrnosoe ycKopeHHe 0. 11 CKopoCTb H3MetteHH• B:JaJtMO.lleHcTBHe TOK3 q" 33pJl..llOB Macca m MoMeHT Httepmrn T 11H.11)'KTllBHOCTb L 3aKoB KynoHa )l{eCTKOCTb npH )l{eCTKOCTb npH BeJ1HqRHa, 1 k KpyqeHHH k o6pam3.ll - paCTJIJKeHHH JJleKTPOeMKOCTH c 3JJCICTpHlleCK3JI nOCTOJIHHaJI CHJ13 F MoMeHT CHilbJ M HarrpJ1JKettHe U CHJIOB3JI xapaK- Ko3<j><j>Hl(HeHT lKH/ll<Oro Ko3<j><j>HlHeHT lKH/IKOro ConporneJ1eH11e RTpeHH• r TpettH• r TepHCTHK3 3JJCK- TJ)H'-ICCKOro nonH 11Maym.c mv MoMeHT HMnynbca fro flOTOK MarHHTHOH HH.11)'KlllH Li - aarrpnceHHOCTb Cynepno3HllHB 3JJCKTpH'-ICCKKX Pa6oTa dA =Fx'dt Pa6oTa dA = Mo.'dt Pa6oTa dA=Uq'dt noneH JlHHHH HanpJ:- MolllHOCTb P=Fx' MOlUHOCTb P=Mo.' MOlUHOCTb P=Uq' )l(CHHOCTH none TO'-IC'-1.HOfO KHeeTH'tecKa• x'2 KHHeTHqecK3.ll o.'2 3ueprHJ1 q'2 3aeprH> m- 3HeprHJI ] - MaTHHTHOro L- 2 2 DOJIJI 2 33pA.ll3, JapJl:iKCH- HOH nDOCKOCTH, nnocKoro KOH- flOTeH[H3JlbH3M 2 floTeH[H3JlhH3.ll 0.2 3tteprn• q2 3Heprn• k!_ :meprn• k - 3J1eKTP1P1ecKoro 2 2 fJQJ]_JI 2C .l(eHcaTopa flep11011 ceo6011HblX flepHOll CB06o/IHblX nep11011 CBOOOllHbiX KOile63HHH ~ KOJ1e6att1tH Jr Kone6a1rnfl T=2n - T=2n - T=2n..fiC k k 011ttopo11Hoe 3JJCKTpH'iCCKOC none CHJta, ,ll,CliCT- Bonttoeoe Bonttosoe Bomrneoe conpoTHeneHHe ~ conpornsneHHe .Jki conpon1BJ1eHHe ~ p= km p= kl p= - c BYIOlUaJI H8 TO- qel.fHhlH JapAA 3nCKTpoCMKOCTb KOHJJ.eACaTopa 3HeprHJI 38p•- HocHTeJJH OcHoaawe laKOHbl TexHH'lecKHe Cpeaa 38pllll0B BOJJLT- &MnepHwe npHMeHeRHll xapaKTepHCTHKH )l(CHHOfO KOHJl.CH- caropa )l;H3JIClfpH'ieclC3JI MeT8JIJlb1 Cso6011ttble I ='!._ I = nevS I 3neKrp<YreXHHK3 3neKTpOHbl R' R=ps, npoHHU3CMOCTb :Lu :~ p = Po(l +cit) R=const p = p0 (l+a/) HaJaauae 3 neKTpO- floJJOJKH- m = kit = - 1- M It :L r3.flh83HOTin3CTHKa~ JIHTbl TellhllbIC H pa<j>HHHJ>OBaHHe OTpKU3- N,.e n MeTaJIJIOB, 3Jlel<Tp0Me- TenbHhle I= U-V, r11e T3JIJIYPrH•, DOJJHpoe- HOHbl r v Ka, TPaeneHHe CHJll.,I CHiia Kynotta (3neKTpO- V - nOTeHI111an no11MpH33!HH 311eKTp011a :;; CT3TU'-ICCKaJ1) "f83bJ 3neKTpOHbJ, mv2 ,:.~ TJJelOUIHH p83pllll: TIOJJmKM- qEI =-- ~Wx peKn3MHhle Tpy6KH, TeJlbBbie H 2 ilOMHHec.u.eHTHblC OTpH[a- IH - 33BHCHT 0 u 11aMDbl. Hctcpa: HCKp. o6pa6oTKa MaTep11a- TeJlbHhle OT HHTeHCHBHOCTH noe. ,Leyra: ceapKa, HOHhl HOHM33TOpa pe3K3, fIJl3BK3. KopoHHblii pa3pllll: Olf.HCTK3 f8308 OT 5 3JJCKTpH1lCC- ":; KaJI CHiia "'~~ ii " CHiia ~,., flopelllla e apHMeceii BaKYYM Jho6ble mv2 :L BblilpHMU.TeJIH, 3apJ1JKeHHble --~ABbJX ycHJllfTeillf, reuepaTo- 1.f3CTltllbl, 2 pbl, 3JleKTpOHHO- IUl.ll)'KTH- ~eeb1e Tpy6KH CHiia AMncpa CHJia pyeMble (OC[Hlll!Orpa<j>bl, 8 BaKYYM TeJJeBH30pb1) (qawe 3JICKTp0Hb1) :;; ynpyrocTH ""'0 CH11a ":;; i5. T}JCHH.sl CTOJJYnpo- Cao6011Hh1e :L 311eKTpOHHXa 80.QHHKH 3IIeKTpOHhl, l=l:J +lpCBJ133HHbJC 3JieKTpOHbl (.lblPKH) -1 "'" CHna no- ~ eepXHOCTHO- "0 ro H3T.sl)l(C- ::;; HIDI 3neKTp03HepreT~Ka flpOH380)1CT80 3JieKTp03Hepn<.H BeTpo:mepreTHKa IlpHJTHBH3.ll 3HepreTHKa '---------~----~----~---+tCoJJHeqtt3Jl 3He reTHKa JJHHHB rrepeMeuHoro TOK3 IloBhJillalOrrurn KDBlleB- ITOHHlK3.JOlllllii tc>PMYJJbl HBHMeHOB8HHe tc>PMYJJW q Cuna TOK3, 3ne- /,IM MeRTTOKa IFl=k1q,llq2I B:JaHMo.n.cHCTeHe F=k'I/2MTOKOB r2 r k=-1- 3aKOH AMnepa k'=~ 47tE0 2n Eo ManntTHaJI no- µoCTOJIHH3JI - ff CHnOBaJI xapaK- B=..!.._E=- repHCTitKa Mar - q ElMTHOf'O IlOJlJI - JM., HHllVKIIHJI .E=E1 +£2+...+£. CynepnoJ~B B= B, +B2+···+B•MarHHTHbrX n011eH JlKHHH MarHHT- HOH HHJIVKl"(HH E=-q- none np•Moro I 4ne0r 2 TOK8, KOnbUCBH,ll- B=µo-- eoro TOKa, con e- 2nR E=-q- li0.H.ll3 B- I 2e0S -µo 2R E=....!L B =µ0nle0S E =const 011nopo11Hoe MaruHTuoe none B= const F=Eq C1111a, ,ll,eHcrsyK>- F=B!Msina Ul3" FIB 3JJCMCllT TOK3 F = lqlvBsin Cl CH11a, ,neiiCTByJO- ma• Ha J],BH)K}'- IJ..IH.ik.H 38.DJl.ll C=!L lfHll)'KTHBHOCTb L = <l> u K3'J'YWKH I cu2 3ueprHJl K31)'WKH L/2 W=-- CTOKOM W=- 2 2 E MarnHTnaJI npo- BE=_!!_ l:l:HU3CMOCTb µ=- E Bo qTO ODKCblB8eT MaTeMBTH-tecKoe HanpaBJlfHHe cHJJw CHJtB ewpa*eHHe CHJILI 3nel<TpOCT3Tif'-ICCKOe • ~ © © ~ •B3aHMO.llCHCTBHe 3JTCK- IFI= jq,llq2JTJ)Hl.JCCKHX. 33pJl.llOB ,1'..e e-4---.4itE0Er2 ~ ..Le ,ll.eiiCTBHC 3JJeKTpuqec- e----p £.xoro llOIIJI Ha TO'iCll- F=qEHhl.ff 3JICICTpH4CCK.HH ft---e38p•.n -,[{eitCTBHe FJT = lqlBvsin a .MRfHHTHOro fFn•I iiDOIIJI Ha .UBHJKYlUHilCJl l3 3JTCKTPH'ieCKHH Jap.sl)l, ,ll.eikTBHe ManntTl:IOfO 1JllOJIJI Ha npoBO,[{HH.K c FA=Bl/sin a l3 TOKOM I B33HMo.neH:creue 11e- Fx =-kx ~tf>OpMKp083JU-lblX TeJl B3aM.MO.LleitcTeHe [;;J:JLTPY- FTP =µN FTPIJ..IHXCJI TeJI 833HMOJJ.CHCTBHC Mone- HanpasneHa no xacaTeJib- KYJI Ha rpaHHUC cpet1,b1 HOH K noeepxHOCTH, nep- F=crl llCHllHKYJIRpHO K JIHHHllM, orpaHH~B3JOIJ..IHM noeepx- HOCTb HHcjlopM84MOHHO- cnpaBO'IH8R ra6nM4a ©000 «"1Hcjlonnacr», 2007 r. : : TPattc<j>opMarop carophl Tpruiclj>opMarop Inepe11aqa 3JICKTp03HeprHH I K aOTpe6HTemo ,__________..lrroeblrn3.JOl!UfH ~ Hmie ,______.. r. MocKsa, KawHpcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru 1IHHHJ1 nOCT01111Horo ron TpaHclj>opMarop I .~ I pTepb! rl_lf_cn_Q;_]bJ0--88HH--C-lJl-e-IITp0"1llCpf1Dl----~L._ 3.,eirrponpllBOll. 3l irrporqlMllS. '.lllerrpolllD. 'l.lCICTpOOCBOllCBlle Ten qmc: 8 1499 94a-93-23
  • 66.
    0 6 PA 3 0 B A H 111 E Teopn11, IlpOHBJICHHe .slBJieHHe O npe11eJ1enue 06'bHCHRIOUl8R B npupo11e llcnOJlb30BSHHe B BBJietrne TeXHHKe HHTep- Cno>KeHHe KorepeHTHhIX ceeTOBbIX BOJIHOB!UI TOOpHll Pa.rzy>KHble UBeTa TOH- <J>epeHUHJI BOJIH, npH KOTOpOM BOJH>lKaeT ye- r10Hresca - <l>pe- KID< DJIOHOK. npoCBeT- CBeTa TQHqReaJI BO epeMeHH HHTep<J>epe11- Hem1. neHHe onTHKH . 11HTep- UHOHH3Jt KapTHHa M3KCH.My-MOB H 3nel<TpOMarHHTHrul <J>epOMeTpbl. MHHHMYMOB oceeuteHHOCTH. TOOP"" M3KCBeJIJia MeTPonorHJ1. Koe- Ycnoem1 KOrepeHTHOCTH: T'pOJlb K3CfCCTB3 nonH- (v1=v2, Ii= qi 1 -qi 2 = const) poeaHHblX H wnH<J>o- B3HtiblX noeepXHOCTeH )J.H<J>paK- Orn6anHe ceera nperulTCTBliUIMH, BOJIHOB!UI TOOpH• rano. )J.H<J>paKUHOHHaJI U.HJI ceera OTKJIOHCHMe OT npJtMOJlHHCHHoro fJOiireuca - <l>pe- peweTKa K3K cneK- pacnpocrpaneHl!JI. YcnoeHe ua6mo- BeWI. 'fJl3JlbHhlH npH60p. d -JD..B na6oparnpnb1x 3neKTJlOM3fHHTHaJI forrorpa<J>Hl! .nemui:: TeOpHll MaKceenna ycnOBHRX: d - A. )J.Hcnep- JaBHCHMOCTb CKOpOCTH cee-ra 8 3neKTJlOHH!UI Teo- Paeyra. CneKTJlOCKon. CHJI CBCT8 eemec-ree OT qaCTOTbl BOJIHLT. 33.BH- pHll Jlopenua Cnek-rpan&m.rii ananHJ AHo- CHMOCTb 00Ka38TCJUI npe.lOMJlCHHJI M3JlbH8>1 OT qaCTOTbl CBeTOBOH BOllHhI. llHCnep- PeJottaHcHoe nornomeHHe ceeTa CHR nonRpH- Bw.neneHHe H3 ecrecreeHHoro cee'T'a 3neKTJlOMarHHTHaJI flon•pOHllbL 3aU,HSI. CB060)lHblX Kone6aHHH c onpe11e- TeopHl! MaKcBenna. flon•pHMeTpbl - onpe- CBeTa neH.HhJM ttanpaeneHHeM 3JleKT}JH - TeopIDI aHH30TJ>O- .n.enemrn KOHUOHTJ>a- qecKoro eeKTopa E nH~eCKMX csoHCTe UHH caxapa, opraHHYe- KpHCTanJJOB CKHX KHCJIOT B paCTBO- pax. 3<j><J>eKT H3MeHCHl1e socnpHHHMaeMoH 1.f3C- 3nelCTpOM3fHRTHilll Onpe11eneHHe eenH"lfH- )J.onnepa TOTbl KOne63HH.K, o6ycnoenennoe TeopHll MaKceenna. Hbl H uanpaenelilill OTHOCHTeJlbHblM JJBH)Kem1eM Ha- Cneu11anbna• Teo- CKOpOCTH nnamrr H 6wonaTeJIJ1 H HCTOlfHHKa CBeTOBblX pm1 OTHOCHTeJlbHO- 3803/l B 3CTJ)OHOMH.H, BOJIH CTH aBTOM06HJJeH H Ca.MO- neroe 3<J><J>eKT !1JJJy«ett11.e CBeT3 3JleK1'pOH3MH, BonHOBIUI TeOpHll C«eT«HKH 4epeHKOBa. "lepeHl<o- llB""'YIID'MHC• CO CKOpOCTblO, npe- fK>li:reHca - <l>pe- Onpe11eneHHe CKOpO- ,ea -Basu- BlJlllaJOJlleH CKOpOCTb ceera B cpe- Heru1. CTH 33pj{)t(eHHbIX. qac- ~1083 11e. 3neKTJlOMafHHTHaJI THU B •llepHOH <l>H3wce. TeopHl! MaKceenna M o11eJJH aToMa: T p y11eoCTH MOlleJJH ToMcoe a : - MOllCJib aTOMa <my.ll,HHI' c HJIOMOM» - Onb!Thl no pacce•HHIO a - qaCTHU )].»<. ,[lK. TOMCOH (1903) --+ Tpy1111.ocru MOlleJIH Pe3ep$op11a: - •.11epHa• MO,)leJJb - ycroli'!HBOCTb aTOMa 3. PeJep<j>op.11 (1911) - JIHHeil"!aT&Je cne1CTpbl •KeanTOBb1e n ocryJiaTbl R. I>op a (1913) I. 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CeMenoe) CaeToeoe BoJHHKHOBe- OnbITbl Jle6e11e- Y'leT HMnynbca OTKnonenne KO- ;:iaeneu11.e HHe CBeTOBO- ea. <l>opMyJibl <j>OTOHOB MeTHbIX XBOCTOB OT ro ,naeneKH.11 MaKceenna y coJIHUa ea eemecreo p = (1 +R)nh- P = (1 +R)ooc C 3<J><J>eKT Pacce•HHe Apace > Ao KoMmo- peHTreHoe- YpaaHeHHe KoM- )J.oKaJaTenbcTeo DTOHa - )J.e6aJI cyrueCTBOB3HHJI <J>oTOHOB H HanH- /!J... = 2h sin2 ~ 'lHJI y HHX 3HeprnH ua cxoro HJ.JIY- qeHWI CB0- 60)IHblMH 3JleKTJlOH3Mll me 2 H 1rnnyn&ca <l>nyK- CHCTeMaTH- 01lblT EoTe <l>opMyna 3HH- )J.oKaJaTenbCTeo T}'3UHJI qecKHe OT- WTeilHa ilJIJI <J>nyK- KBaHTOBOH npHpo- <J>OTOHOB KJlOHeHHJI OT Onb!T Ho<J><J>e - ryaUHH nnoTHOCTH llbl ceeTa np.11 ero cpe11nero )J.o6poHpaeoea 3HeprHH HJnyqe- pacnpoCTJlaHeHHH JHaqeHHJI RH.SI a6COJIJOTHO «Hcna <!>OTo- qepnoro Tena H HOB ceeroeoro ,naene- ffilll TpyllHOCTH TeopHH H. Eopa )J.ano 06'bJ1CHeHHe cne1CTpa Toni.Ro aToMa eo11opo.11a r1m0Te3a 0 BOlIHOBblX CBOHCTB8X 3JlelCTpOHOB. 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  • 67.
    I ATOMHOe llllpO IICocrns arnMHoro 1111pa KaK o6beKT H3y<teH.Hll I IIlpoToHHo-HeiITpottttaJI Mo11em, ll)lpa: A = Z + N I ! ITHnH'fHbJe <!>HJH'leCKHe irnnemu1 paccMaTJlirnaeMoii 06nacn1 I • •PA]UfOAKTHBHOCTb 5IJJ,EPHb!E PEAKI.IJlli 51)1epHbie CHJ!bl: a. - pacna11, 13 - pacna)I 1 ;N+;He~ 1 ~o+:H - 6JII1JKO)leiiCTBHe; y - H3Jl)"leHHe npH a. -, 13 - pacna11ax - Japll)IOBaJI HeJaBRCHMOCTh; 3axoH pa)IHOaKTHBttoro pacna11a 21Al+4He~3op+ 1n - o6MeHHblH xapaKTep BJaHMO)leHCTBHll. I 13 2 15 0 N=N 2-r HJIH N = N0 e-"' 1 ~H+~H~~He+~n l0 J. 13- 13- 3tteprHll CBllJH Ec8 =(Zmp+ Nmn- m.)c2 IlpHMCReHHe llBJleHHii 238U+ 1 ~239u~239Np.4239Pu E • n on 92 93 94 Y11eJTuaaJ1 :meprm1 CBJIJH MJ0Tonb1. liHonornqecKoe 11eiiCTBHe HJJI)'- I.(enHble 1111epttb1e peaxqHH A 'leHKH H Jall(HTa OT HHX. 5l11epRhiii peax- 235U H 239PuTop. 5l11epttaJ1 :meprenn<a 92 94 ffa3eauue ro11 A1nop CocTae R11pa qyo Ofi-LRCHReT Tpy!IHOCTH MOiie.JiU IlpOTOHH0-3JleKTPOHHaJI 110 M.KiopH 5ltlpo COCTOHT HJ npOTOHOB H Macey H Japl!ll l!llPa CllHHOBaJI aJOTRaJI KaTaCTJJO<!>a 1; N (cIIHH 1932 3JICKTPOHOB YCTOH'lHBOCTb l!llpa (Np=A, N,=A-Z) ll!lpa ueJlhlii, a COCTaBJIJIJOIIIHX ero 14 npoTOHOB H 7 3JleKTPOHOB - nonyueJlh!H) IlpOTOHHO-HeHTJlOHHaJI 1932 ,ll;. ,ll;. fuatteHKO 5l)lpo COCTOHT HJ npoTOHOB H Macey "' 3ap1111 J111pa HeT CTJlOfOH TeOpITTI ll)lepHb!X CHJI 8. reiiJeH6epr HeHTJlOHOB C~ecTBoBaHHe HJOTonos KaneJ1bHaJ1 MOlleJlb Hau111euoeattue 'IBCTHO <l>OTOH 3JICKT)>OHHOC HCHTJJHHO MJoOHROe :0 aeiiTpHHO a: Tay-HeiiTpHHO ~i::; 3neKTpOH Mloott Tay-nenToH IlH-MeJORhl :ii Ka-MeJOHbl a: 0 "'.., ~ 3Ta-HyJTh- MeJOH ~ IIlpoTOH 0 HyKJ1ou HeiiTpOB Q.. "1'. J111M611a-<( rHIIepoe :ii CttrMa- a: 0 ranepott c...,c: :s: ~ Kcu- rnnepoH Ol.lera-MJ.tttyc- rnnepott (Np=Z, N.=A-Z) 1936 51. M. <l>pettKeJTh 5l11po npe11cTaBJ1lleT co6oli uia- Hacb1111ettHOCTu ll)lepttblX CHJI 3aplllKeHHaJI lKHllKOCTb IIO)l'IHHJ!eTCll H. I>op poo6paJttyKl KanrrK> csepxnnoT- MexaHHJM 11enettHll llllPa J8KOHaM KBaHTOBOH <!>HJHKH HOH JaplllKeHHOH lKH)IKOCTH 3HeprHJO CBllJH CnMBOJJ Macca B MBCCBX BHTH- 'IBCTH- :meKTpo- 'IBCTH- BM3B OLI I.ILi ua m, v 0 0 v. v. 0 0 vµ vµ 0 0 v, v, 0 , 0 e e+ I 0,511 µ - µ+ 207 105,66 -c- ,+ 3492 1782 no 264,l 134,96 7t+ 7t - 273,1 139,57 K+ r 966,4 493,67 Ko Ko 974,1 437,7 110 1074 548,8 p p 1836,1 933,28 n n 1838,6 939,57 Ao x_o 2183,1 1115,6 L+ f + 2327,6 1189,4 Lo f O 2333,6 1192,5 L- f- 2343,1 1197,4 30 3 0 2572,8 1314,9 ~ -- 2585,6 1321,3.::. ff I n- 3273 16/2.2 YCTOii'IHBOCTh ll)lpa Cnuue 3neKTpu'le- e)IHHH- CKHH 3BpRll BpeMR B 3JleMeH- *H3HH, nax h TBpHLIX c lBpRllBX e I 0 Crn61rnett 1/2 0 CTa6HJibHO 1/2 0 CTa61iJibHO 112 0 Crn6HJibHO 112 -1 1 Crn6HJ1eH 112 -1 I 2,2. 10-6 1/2 -1 I 1,46. 10-12 0 0 1,83. 10-16 0 I -1 2,6. 10-8 0 I -I 1,2 . 10-8 0 0 K~ -s,9.10-11 Kf-s.2.10-8 0 0 2,4. 10-19 112 l -1 Crn6Hnett (?) 1/2 0 103 1/2 0 2,63 · 10-IO 112 I -I 8 · 10-Il 112 0 5,8 . 10·20 112 -1 I 1,48 · 10-IO 1/2 0 2,9 · 10-lO 1'2 -1 I 1,64 · 10-IO 32 -1 I 8.2. 10-11 OCHOBHblE CBOHCTBA HecTa6HJThHOCTb (CTa6HJlbHbI: <!>OTOH, 3JleKTpOH, npoTOB, HeHTJllIBO) B3llHMOlleiiCTBHe H BJllHMOIIpespa~aeMOCTb CymeCTBOBaHHe aHTH'laCTHI( CnoJKHoe CTPOett11e 6oJiblIIHHCTBa qacTHU T ( 3JIEMEHTAPHhIE lJACTiflU>I ) ! CPE,ll;CTBA OIIBCAHllil ---+TEOPETw:IBCKME 3aKOHWCOXpatteHHl! IlpHHl.(Hllbl CHMMeTpHH 3aKOHbl <i>YHJJ.aMeHTaJThHblX B33HMOlleHCTBIIB ---+ 3KCITEPMMEHTAJlbHblE YCKOpHTeJIH Cl.(HHTH.llJIJlllHOHHwecqeT'IHKH KaMepa BHJlbCOHa C'leT'IHKH reiirepa - MloJIJiepa qepeHKOBCKHeCqeT'fHKH MeTOll TOnCTocnoilHb!X <t>oTOJMYJibCHii IlyJWpbKOBall KaMepa ~H<j>OpMa~MOHHO­ cnpaBO'IH3R ra6nM~a © 000 · ~Hcjmnnacr», 2007 r. r. MocKea, KawMpcKoe wocce, 21 E-mail: mail@infoplast.ru http://www.infoplast.ru ~en Q)3J(C'. 8 1499 940-93-23 "'0 ..... 0 "'
  • 68.
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  • 69.
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  • 70.
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  • 71.
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  • 72.
    • • UH4'0n/ACT n.· www.infoplast.ru K11acc1r1cp1r1Ka41r1H Heconeo6pa3yt0L111t1e(6e3pa3I11t14Hb1e): N20, NO, CO? coneo6pa3yt0L111t1e OCHOBHble aMQJOTepHble Klt1CJ10THble I,II II-IV V-Vll MexOy MexOy HMexOy MexOy nepex. +7 Na20 ZnO co2 Mn20 7 Cao Al20 3 S03 c~o +3 +6 Cr2 0 3 Cr03 OKCIAA Cr(ll) OKCIAA Cr(111) OKCIAA Cr(VI) ra3 >K1t1AK. C02 H20 S02 so3 NO Cl20 1 N02 Me HMe <!>"13"1'-leCKMe CBOHCTBa TeepA. OCHOBHble aMQJOTepHble Si02 P20 s Cr03 MexOy (Lll•I Ll..1-3.) Klt1CJ10THble OKCIA,Qbl ~ +H 02 paCTBOp Me(OH)xJ. Hx03y Me30y! Me(N03)x (Mg-Cu) Klt1CI10THbl~ OKCIAA H2 0 -+ K-Ta (p.) Ll..lefl04b -- COI1b + HzO aMQJOTepHbl~ I H20 -- Llleno4b OCHOBHO~ OKCIAA Klt1CI10Ta 7 COilb + H20 H J... Me+ H 0? ? O,QHOocHOBHble MHOrOocHOBHb1e HF (nnae1r1Koeafl), HN03 H2S04 , H3PO4 6ECKV1Cn OPOAH blE HCI, HBr, H2S CV1nbHblE (a-+1) H2 S04 , HCI, HJ, KVICnOPO,QOCO.QEP>KA~VIE (r1t1APOKC1t1Abl) HCIO4 (xnopHafl), H3B03(6opHafl) cnA5blE (a-o) HMn04 (MapraH1..4oeafl) H2Cr04 (xpoMoeafl), HF, H2S, H2S03, HN02 (a30Tlr1CTafl), HCIO (xnopHoeaT1t1CTafl) no11y'-leH1r1e <!>M3"1'-leCKMe CBOMCTBa H2+ HMe -+ Hx3f BKYc! P-pbl K1t1cnoTHbl~ + H 0 -+ H 30 (p ) >K1t1AK. TeepA. ra3oe OKCIAA 2 x Y · H2S04 ~ HCI, HBr, K1t1cn0Ta + conb -+ K1t1cn0Ta + conb HN03 H3P04 H2S, (! 11111111 f ) HCl03 H3 B03 HCN S0 + 2HN03 -+ H SO + 2NOT (c1t1H1t1I1bHafl) BOCCT. OKl1CJ1. 2 4 H20 H2C03 { KOHLI. H2S0, HNO OKl1CJ1. 3 XMMM'-leCK"1e CBOHCTBa H 30 11 ~-P H++ 30 x- cTyneH4aTo x y +- x y a.1>a.2 M e (Ao H2) -+ .Q H2 i Me -+r- H2 0 +? I-IV ~ MexOy -+ Q+ H20 OCHOBaH1t1e -+ HzO COJ1b -+ {) J. KIACilOTa Hx30Y -+ Klt1CJ10THbl~ OKCIAA + H20 16HCl- 1 + 2KMn04 -+ 2MnCl2 + 5CI~ + 2KCI + 8H20 BOCCT. P.s1A HanpH>KeHMH MeTa1111oe K Ca Na Mg Al Mn Zn Cr Fe Ni Sn Pb H2 Cu Hg Ag pt Au - yeen1t14eH1t1e BOCCTaHOBlt1TeJ1bHblX CBO~CTB - - ~aCT:b 1 Knacc1r1cp1r1Ka41r1.s1 CPE.QHV1E Mex3y Mex30y NaCl KV1CnblE (H) OCHOBHblE (OH) MexHz3y Mex(OH)z3y KHC03 MgOHCI Al2(S04) 3 NH4N03 r1t1APOKap60HaT K r1t1,QpOKcoxnop1t1,Q Mg Ca(H2P04 ) 2 Fe(OH)2N03 HVITpaT aMMOHVlfl A1t1r1t1Apo¢oc¢aT Ca A1t1r1t1APOKCOHvtTpaT Fe(lll) .QBOLliHblE KOMnn EKCHblE Me1Me230y [Cu(NH3)4 ]S04 NaCl• KCI cynbQJaT K2NaP04 TeTpaaM1t1H Cu (II) opTo¢oc¢aT Na[Al(OH)4]+:! Kafl1t1fl-HaTp1t1fl ;::! Na++[Al(OH)4 ]- <J>1r131r1yecK1r1e CBOHCTBa TsepAbre + H20 ~ pacTsop1t1Mb1, Ma.11opacTsop1t1Mbl, HepacTsopvtMbl nony'-leHMe OCHOBaH1t1e " + H20 Klt1CJ10Ta + OCHOBHble MexOy -+ .J.I + H20 MeaKT r- + H2i L11eno4b + KVICilOTHble ..., + H 0 OKC1t1Abl 0 2 Klt1CJ10Ta + KVICilOTa conb + L11e1104b I + ocHosaH1r1e ! COJ1b (p.) ,,/ + COJ1b ! Me + HMe -+ Me.3y X1r1M1r1-..ecK11te ceoMcTaa (p.) (p.) (p.) Me(aKT1t1BHee)--+ Klt1CJ10Ta Ll..leflOYb COilb (p.) - --+ Me(M.aKT)! KVICilOTa OCHOBaH1t1eJ. COI1b ~ nH2 0 H 2 0 r11Apon1.13 , • nH 2 0 (Kp1.1crannor1.1,qpar) to !Mex30Y 0 MexOy + HMexOy Me(N03)x ( to • (NH4)x3 t +2 2Fe Cl2 + Cl2 BOCCT. 2Kl-1 + Cl2 BOCCT. -+ 2Fe+3 Cl 3 0 ..... 12 + 2KCI 2KMn+70 4 +16HCI -+ 2Mn+2 Cl2 + 5Cl2 + 2KCI + 8H2 0 OKl1Cn. o 4Fe+2 s ·1 + 11 o .!.. 2Fe+303 + 8S+4 0 i BOCCT. 2 o 2 2 2 N'3 H NO .!. N° i + 2H 04 2 2 2 rMAPOTIM3 Pa311o>KeH1t1e con1r1 BOAO~ c 06pa3osaH1t1eM cna6oro 311eKTpon1t1Ta. 1 .--- CQflb ~l Clt1J1bH. Klt1CilOTa cna6. 0CHOBaH1t1e r1t1Apon1113 no KaT1t10HY K"• Kn++HOH -~ KOH(n-1 )++H+ cna6. cpe,qa 3neKTpon1.1r K1<1cnaS1 Clt1J1bHOe OCHOBaHvte cna6. KVICilOTa r1t1APOI11t13 no aHVIOHY An- An-+H+OH+:!HA(n+1 )-+0H- cna6. cpe,qa 3neKTpon1.1r L11enoYHaSl cna6. 0CHOBaH1t1e cna6. KVICilOTa no Kn+IA An- K"++A""+H+OH"+:!KOH(n-1 )++HA(n+1 )- cna6b1e 311eKTpo1111rb1 cpe,qa HeiilrpanbHaSl rvtApOI11t13 yc1t1J11t1Ba10T A06asneHlt19M BOAbl, HarpesaHlt19M CIACTeMbl ..
  • 73.
    NaOH. KOH, NH;.OHCa(OH)2' Cu(OH)2' Al(OH)3 <l>M3Ml.feCKMe CBOHCTBa TaepAble OCHOBaHll15l non~eHMe -+ ~eno4b + H2l ~eJl04b HEPi-C~BOPv r~ b E Cu(OH)2, Fe(OH)2, Fe(OH)3 PACTBOP~MblE (~enoY 111 ) LiOH, KOH, Ba(OH)2, Ca(OH)2 + H20 ~ 3J19KTPOJ11113 BOAHblX paCTBOpos conei:i ~eJ104HblX Me 2NaCI + 2H20 1. Cl2 + H2 + 2NaOH ~0110Yb CV1JlbHblE (a-+1) ~e1104111 CJ1A5blE (a-+O) HepacTsop111Mb1e, NH40H XMMM"'leCK"'1e CBOMCTBa Me(OH)x KlllCJlOTa v KlllCJlOTHbllll OKClllA COJlb (p.) eAK111e pacTaopb1 L11e1104e~ COJlb (p.) + ~eJ104b -+ COJlb + OCHOBaH111ei Me(OH)2 + 2HCI OCH.CB-Ba Me(OH)2 + 2H+ AMQ>oTepHble rMAPOKCMAbl Mef O f H + 1- 0 + H M 2+ 20H- H : : OH- 2H+ M 0 2 - [M (OH) ]2 -e + . .....................=: ~---··-····--·:• + e eB KlllCilOlll B l!.leflOYHOlll 2 4 cpe.Qe cpe,ae -+ MeCl2 + 2H2 0 -+ Me2 + + 2H 02 • Me(OH)2+ 2NaOH Kl1C!l. CB-Ba 2NaOH + Cl~ -+ Nacr 1 + NaCl+ 1 0 + H20 -+ Na2Me02 + 2H2 0 TOYHee: -+ Meo 2 - + 2H o Me(OH)2 + 2NaOH -+ Na2 [Me 2 +(0H)4 ] 2 Kll!Cfl. CB-Ba OKHCJ1. BOCCT. Me(OH)2 + 20H. 2 2 Me(OH)2+ 20H- -+ [Me(OH)4 ] 2 - 1887 r. CaaHre AppeHvtyc //1. A. Ka6nyKoa np111 paCTBOpeHll1111 B BOA9 (11111111 pacn11aa11eHL-1111) 3J19KTpOJ1111Tbl pacnaAalOTC5l Ha nono>K111TeJlbHO 111 0Tp1111..1aTeJlbHO 3ap5l>KeHHb1e 1110Hb1 (nOABepralOTC5l aneKTpo11111T111- 4ecKo~ A111cco1..1111a1..1111111). KOHf..19HTpaf..11115l 1110HOB B paCTBOpax 3aBll1CL-1T OT Toro, HaCKOJlbKO nOJlHO AaHHbl~ aneKTpo11111T Alllcco1..1111111pyeT Ha 1110Hb1. HE3J1EKTPOJ11f1Tbl: 3J1EKTPOJ11f1Tbl: 60JlbWlllHCTBO opraHll149CKll1X B9U9CTB, H9M9T8J1Jlbl, M9TaJ1Jlbl Kll1CJ10Tbl, OCHOBaHll15l, COJllll (npoBOA5lT 311. TOK B pacTaopax, pacnnasax) Et) -+ KaTOA- 8 -+ 8HOA + CreneHb ,[lMCC04vta4vtvt (a) - OTHOWeH111e 4111CJ1a pacnaBWll1XC5l Ha 1110Hbl MOJleKyn (n) K 06L11eMy 4111CJ1Y paCTBOpeHHblX MOJleKyn (N): na = - NL-1 Bb1pa>KaeTC5l s AOJ15lX ep.111Hll1'-1bl 11111111 a npo1..1eHTax (a<0,03 - cna6b1e; 0,03<a<0,3 - cpep.H111e; a>0,3 - c11111bHb1e aneKTpo11111Tb1). CTeneHb p.111cco1..1111a1..1111111 3aa111c111T OT np111pOAbl aellleCTBa, KOH'-1eHTpa1..1111111 pacTaopa, A06aaneH1115l 1110Hoa. KoHCT8HTa ,[lMCC04vta4vtvt (KAlllC) - OTHOWeH111e npOV13Bep.eHll15l paBHOBeCHblX KOHf..leHTpal_VI~ 1110HOB 8 CTeneHll1 COOTB9TCTBYIOU111X CTeXll10M9TPV1- 4eCKV1X Koacpcp1111..1111eHTOB K KOHf..1eHTpa1..1111111 H9A111CCOf..1111111poaaHHblX MOJleKyJl. _ [K+][A] . K.Q"1C.- [AK] • BOAOPOAHblM noKa3aTenb pH=-1g[H+] [H+]=[OH-] Hei:1TpanbHa5l pH=7 [H+]>[OH-] KV1CJ1a5l pH<7 [H+]<[OH-] Uell04Ha5l pH>7 oo- o+Z> o+ H 1os0 H rMAPOKCMAbl KvtCJlOTbl 0CHOB8HVl5l ~ ,QVlnOJlb Hx30y +-+ H+ + H30y II H30y +-+ H+ + 30y- Hx30y +-+ xH++ 30y- Me(OH)x +-+ [MeOH]++OH- 11 MeOH+ ..... Mex+ +OH- Me(OH)x +-+ Mex+ + xOH- cx.,>CX.11 AMcpoTepHble Mef Of H 1- 0 + H + - K = [H ][OH ] K = [H+][OH-]=1 o-14 Al-IC. [H20 ] ~ H~ MexaHM3M 3neKTponMTM"'leCKOM AMCco4"'1a4MM a pacnnase + + ltlOHbl 0 ··+t Kl!ICJlble I Me(H3) ..... Me++ H32- ll H3 2 -..... H++ 32 • ConM OcHoBHb1e [MeOH]3 ..... MeOH++ 3 · 11 MeOH+ ..... Me2 ++OH- Me(H3) +-+ Me++H++ 32 • Me0H3 - Me2++OH-+ 3 - CX.1 ~ex.II Cpe.qHvte Mex3y +-+ xMey++ y3x- + ' ' OH- Me2++ 20H-~-----tt____:J L--------·--·:+ 2H++Meo2 · [Me(OH) ]2 - s KlllC!lOlll B L!.19JlOYHOlll 2 4 cpe.ae cpe,ae H+ Li+ NH4+ K+ Na+ Ag+Ba2+Ca2+Mg2+zn2+Mn2 ' Cu2 • cu+ OH- p p p p - p H H H H H NOi p p p p p p p p p p p p p F- p p p p p p H H H - c1- p p p p p H p p p p p p p Br - p p p p p H p p p p p p - ,- p p p p p H p p p p p - - S£ p p p p p H - - - H H H - so~· p p p p p H - H so~· p p p p p H p p p p p co~· p p p p p H H - H H - - SiO~· H - - p p H H H H H - - Po:· p H p p p H H H H H H H H cro~· p p p p p H H ,, p H H H - CH3COO- p p p p p p p p p p p p p Hg• Hg2+ Pb2+Fe2+ Fe3+ Al3+ - - H H H H p p p p p p H H p p H p p p p H '1 ~ p p p H - H p p p H H H H H - H - H - - lP p H p p p H H H H H - - - H H - - H H H H H H - - H - - - p p p p p p Cr3+ 8j3+Sn2+ H H H p p - p H p p - p p - p - - - H H - H H p p p - H - - H - H H H - H - p p p Sr2 • p p p p p H H H H H ~ p p M H - - pacTsop111Mb1e (> 1Or s 1000 r H20) - ManopaCTBOpVIMble (OT 10 .qo 0,01 r B 1000 r H20 ) - HepacTaop111Mb1e (< 0,01 r s 1000 r H20 ) v - pa311ara10TC5l aop.0111 11111vi He cyllleCTBYIOT MHcjJopMa4110HHo-cnpaao~HaR ra6n114a © 000 «MHcjJonnacr", 2004 r. MocKaa, Kaw11pcKoe wocce, 21 E-mail: mail@infoplast ru Http:llwww.infoplast ru Ten.: (095) 320-94-89 <1JaKc: (095) 320-94-88 no,qnucaHo a ne~arb 25.08.05. T11pa>1< 40003K3. 3aKa3 N92103. "13,qarenb 000 «MHcf>onnacr", MocKaa, Kaw11pcxoe wocce, 21. TunorparjJ11R 000 «Busa-Crap». 107023, MocKaa. yn. 3neKrpo3aao,qcKaR, 20 ..
  • 74.
    www,infoplast.ru CoepeMeHHble npeACTaeneHMfl1911 r.,3 . Pe3epcpopA ~~ 1913 r., H. cop ~ 1932 r., A-llleaHeHKO Z+N=A m CP)=1 m (0 n)=1 m (e)=1 / 1840 n. A9 opoi.1nb - ABOi.1CTBeHHa5l np11p0Aa 3neKTpOHa: eonHa 11 4acrn4a. ATOMbl OAHOro :meMeHTa, 11M9- IOLl.1"19 OA"1HaKoeoe 411cno npoToHoe, HO pa3nl14HOe 411Cno Hei.1TpOHOB. 1H- npor11i1 3HepreTHY9CKMe ypOBHM n=123 4 5 6 7 maBHOe KB8HTOBOe YMCno (YAM9Hl19 e OT "'APa) I e=2n2 => 3HeprernYeCKl19 nOAYPOBHl1 => Op611T8JH1 => e ~H - p,eillrep11i1 1=0, 1... n-1 s p d f ~H - rp11r11i1 op611TanbHOe KB8HTOBOe Yl1Cno (cpopMa op611rnn11) CnMHOBOe KB8HTOBOe YMCnO ~AepHble peaK4MM MarHMTHOe KBaHTOeoe 411cno: m=21+1 (op11eHTaL1Mfl e npoCTpaHCTee) Op611TanbHOe KBaHTOBOe Yl1Cno: 0 2 3 B11A op611Tan11 S p d f np11H4Mnbl 38nOnHeHMfl op6MT8neiii 3nBKTpOH8MM 1. np11H411n Ml1Hl1MYMB 3Hepr11W 1s<2S<2p<3S<3p<4S<3d<4p<5S<4d<5p<6S<4f- -5d<6p<7S<5f-6d<7p Ecm'1 aneMeHT 11cnycKaeT a-Ya- crn4y, ero npOAYKTOM 5lBn5leTC5l aneMeHT, pacnono)f(eHHb1i.1 Ha 2 KneTKl1 neeee, ~-Yacrn4y - Ha OAHY KneTKY npaeee. Ha nOAYPOBHe: ***gi~~HH~ee n=1 , :=0, Ha ypoeHe ··· 1s ·· op61o1rnnb (:) 2. np11H411n naynw B Ka)f(AOi.1 aTOMHOi.1 op611rnn11 MO)f(9T pa3- Mell.laTbC5l MaKCl1ManbHO ABB aneKTPOHa. 3. npaa11no XyHp,a: mmm .'-- ' t • • I a -pacna,o, n=2, :=1 , Ha ypoeHe ···2s+2p ···(:::) op61>1Tan1o1 n=3, :=2, Ha ypoeHe ··· 3s+3p+3d (V) op61>1Tanei.1 MBKCl1ManbHbli.1 cn11H aTOMa: ITIIIIl ~ ••• ••• neplllOAlll"leCKa~ ClllCTeMa Xl.1Mlll"leCKlllX 3fleMeHTOB ,Q. Ill. MeHAeneeea 1829 r. , Ao6epeillep - BblAemm TP11aAbl 3neMeHTOB. 1864 r., Meillep - 06b9A11Hl1n 3neMeHTbl B COOTB9TCTBl111 c X11MW-19CKl1Ml1 CBOi.1CTBaMl1. 1865 r., Hbl0fl9HP,C - TeOpl15l OKTaB. CoepeMeHH&fl ci>opMyn11poeKa nepMOAMYeCKoro 38KOH8. 1869 r., MeHp,eneea - B ocHoee aTOMHa5l Macca. nep11op,114eCKl1H 3BKOH: CBOi.iCTBa npOCTblX Ten, a TalOKe CBOi.iCTBa C09A11H9Hl1i.1 3neMeHTOB Ha- XOA5lTC5l B nep110A1149CKOi.1 3aBl1Cl1MOCTl1 OT aTOMHblX B9COB 3neMeHTOB. Ceoi.icTea x11M11YecK11x aneMeHTOB, a TalOKe CBOi.iCTBa C09Al>IH9Hl1i.1 o6pa30BaHHblX 3Tl1Ml1 ane- M9HTaMl1, HaXOA5lTC5l B nep110A1>149CKOi.1 3aBl>tCl>t- MOCTl1 OT 3ap5lAOB aTOMOB. ] g:,.Cl. "c: Ill H LI mm11il ~ 6.941 Na I "" HBTpMM ~ 22.99 K R,0 11 19 rpynnbl3neMeHTOB Ill IV V VI VII RO R20 , RH4 R02 RH, R20 5 RH2 RO, RH R20 7 Be 6epMJmMM ; 9.0122 4 B 6op = 10.811 5 c N yrnepoA 830T ~ 12.011 ~ 14.007 0 KMCllOPOA ~ 15.999 Mg 12 Al 13 Si 14 P 15 s 16 1 M8rtu1M t 24.32 2 aJ110MMHi.1~ l 26.092 21 l KpeMHM'1 ' ¢>oc¢iop ~ 28.086 : 30.974 5 cepa i 32.064 Sc 22 Tl 23 v 24 F ¢oT0p- ~ 18.998 Cl e Xl10p I 35.453 17 Cr 25 Mn VIII R04 28 Ni IV ! KBnMM 39.102 : ~ .., , CK8H,Qlll~ ~o 44.956 I TlllT8H ~1 47.956 : BBHSAlllM ~2 50.941 : xpoM ~3 51 .996 : Mapratte1...1 54.938 26 Felf, >Keneao ~e : 55.848 : 21 Co'IK068TlbT ~8 58.933 : H.1K0Ilb 58.7 v .'."' .K 2 29 Cu M0,Qb ~I 63.546 : 30 Zn Ga Ll.1HK fanJ1.1M 65.37 69.72 31 Ge ,: repMaH1o1M : 72.59 32 As 1: MblWbSlK : 74.922 33 Se 1~ ce.neH I 78.96 34 Br ,: 6pOM I 19.904 35 ' ".' , 44 Ru1 I'45 ;: pyreHM~ :: ~ 101 .07 2 Y l:'• 40 Zr 1:,''2 41 Nb , 42 Mo ~3 43 Tc ITTTpHM l.1"1PKOHlllH HH06111M i: MOI11116AeH 1e T0XH01.1HH 88.906 a 91.22 92.906 a 95.94 I (99] Rh:1· 46 Pdpo,QMH i: nannSAlllH 0 Rb 31,Sr 38 ,,39 VI : ~M ,: CTJ>OHL4MH ,: ~. ~ RS.468 I e1.62 : I 102.906 a 106.4 530 , 47 Ag l,., 48 Cd In VII : ~= cepe6po Ka,QMlllH lo1H,qlo1&11 49 ~1, !~BO 50 ~!, !~bMa 51 :!, ~~nyp 52 ~1, ~OA ' ""~ : 107.868 : 112.41 114.82 118.69 121.75 127.6 126.905 l VIII 0 ··.', CsLl93MM 132905 55 : "·:. Ba 15apMli 137.34 ix ~~ ~::: 19 Au h80 ~:.:~ i' x 0 0:' Fr 87 ' =·=.· CIJpaHl.IMM i [2231 Ra Pai:l<ii (226) 57-71 La-Lu fl8HTSHOHAbl !~ 12 Hf ;:,:• 13 Ta ~2 14 W ~:',', 15 Re k,·, 1s •," ra¢>H1o1H T8HTan ~ eonbtj:lpaM peHlllM 11a.49 180.948 I 183.85 186.201 i Os ll, 11 Ir I:, 78 Pt OCMlllH ~ lllPM.QlllH ~ nnaT111Ha 100.2 I 192.22 : 195.09 Hg Tl s1 h,::, Pb 82 h,:, Bi 83 h,',s Po 84 1: At PTYTb rann111M ce111Het.1 e111cMyr nonott111M tl acrar 200.s9 204_31 201.19 : 208.98 I [2101 I [2101 88 J..".. 89-103 Ac-(Lr) ""'""""'"" il 104 R! !~ 105 Db ~ 10& Sg h101 11 peaep¢op.QMM ~: AY6H1o1M ~: CM6op1111M ~: I 12611 : (2021 : l263J I 85 1~ ll l Bh ~ 108 Hs lh109 Mt:lh110 Os 6op1o1H ~ xaccHK U MeKTHep111'1 ~: ,ciapMcra,r:rrnYM [262] : [265] : {266] ~ [269] Ha renMM 4.003 Ne H80H 20.179 Ar aproH 39.948 Kr t<p.1nTOH 83.8 Xe KeeHOH 131.3 Rn PCIAOH (222) 10 18 36 ."l 54 :! l 86 ~ I 57 la : sa Ce : 59 Pr I 60 Nd i: fl8HT8H l: 1.1ep111K U~MM ~ H80AlllM I 63 Eu : 64 Gd ~ 65 T~ L66 D)'. L67 H~ L68 E~ !,&9 T~ L10 Y~ !, 11 L~ ~ eepomtK ~ ra.QOJ1MHMl°1 11 rep6111o1 11 ,ci111cnpo3HH 11 ronbMllllll ,, ap6111111 11 ryn 1o1111 11 ITTTep6Hvi ,, more1.11111o1 : 138.906 : 140.12 : 140.908 2 144.24 : 151 .00 : 1s1.2s : 1sa.e26 i i s2.s : 164.93 l 161.20 : 1ss.e34 l 113.04 : 114.97 I u Ac :, 90 Th I 91 Pa I 92 U I 93 Np l 94 Pu l 95 Am l 96 Cm I 97 Bk l 98 Cf I 99 Es l 100 Fm I 101 Md l 102 No : 103 Lr r. SKTMHMM r. TopMM HnpoTalm!MMM ~ ypaH ft HBITTyHMH ennyroHMl4 ~ aMepH~M ~ KtOpMM ft 6epKnMM ft~lllK aMtwreMHMM e¢>epMMM i M8HASn&BMM ~ Ho6e.nMM ~ noypeHCMM : (227] : 232.038 : (231} : 238.29 : (237) : [244] : [243} : [247] : [247] : (251) : [254] : [257] : (258] : [259] : [260] B nep1110,qe: B rpynne: ,Q. Ill. MeHAeneee 1834 - 1907 rr. nop$1AKOB9fi'il HOMep ClllMBOO aneM0HTa 25 Mn ~2 MapraH0LI ; 54.938 Onioc111renbH8$1 aTOMHasl Macca Pacnpe,QeneHHe aneKTpoHOB no CJlOSIM D s - 3neMeHTbl D p -3J19M6HTbl D d -3110M6HTbl rn f - 3fleMeHTI:.I HoMep 3neMeHTa: 3aP"'A flApa, cyMMapHoe 41>1Cfl0 aneKTPOHOB, 411Cno npOTOHOB. HoMep nep1110,qa: Y1>1cno 3HeprernYeCK"1X yposHeii. Mei - MeTanna.1YecK11e caoiicrna YMSHbWatoTCfl; Met - MeTann11YecK11e caoiicrna yeena.1Y11sat0Tc5l; HoMep rpynnb1: 41-!cno saneHTHblX aneKTpOHOB, MaKC"1ManbHYIO nonO)f("1T9nbHYIO CTeneHb OK"1CneH"15l (CO) 3ap51A "'APa ysen11Y1>1saeTcfl; paA11yc aTOMa yMeHbwaeTcfl; •mcno BH9WH"1X aneKTPOHOB ysen"1411BaeTCfl; npOYHee 11X CBfl3b c "'APOM. sapflA "'APa ysen1>1Ya.1saeTcfl; paA"1YC aTOMa yysenH4"1BaeTCfl; 4"1Cno BH9WH"1X aneKTpOHOB noCTOflHHO; cna6ee 11X CBS'l3b c "'APOM.
  • 75.
    3ro ~ AfJyxaTOMOB, ocy114ecTem1eMoe nyre M o6MeHa 3neKTpoHaM11. ()()pa3oeattMe ~Koiii CBSl3M - OObeAHH0Hl10 aTOMOB B Monet<ynbl. X11Ml140CKaSI CBSl3b - Q:>opMa Bb111rpblwa 3Hepf"Ml1 ~ npM 00pa3088Hl111 XMMM40CKOM CBSl3M aTOMbl CTp0MSITCSI np1106pecrn YCTOM411BYIO BOCbMl13fl0KTpoHHYIO (11n11 AByx3neKTpoH- ~ HYIO) BHeWHIOIO o6on04t<y, COOTB0TCTBYIOU4YIO CTP00Hl1IO aTOMa 6n11:>Kai1Ujero 11H0pTHOro ra3a (npae11no OKTeTa). Pa3nM48IOT Cfl9AYIOU4119 B11Abl Xl1Ml140CKOM CBSl311 : KOaaneHTHaR (nonSlpHaSI 11 HenonS1pHaS1; o6MeHH8SI 11 AOHOPH0-8K4enTOPH8SI), HOHHaJI, ao,qo- p<J,qHaJ/ 111.1erannw-1ecKaJ1. lilOHbl - 3TO 3apSl:>K0HHble 4aCTl14bl, B KOTOpb1e npeepa114a10TCSI aTOMbl B pe- 3ynbTaTe OTAa411 11n11 npl1C00A11H0Hl1SI 3neKTpOHOB. llTOHHaR CBR3b - npeA0flbHbllil cny- 4ai1 KOBaneHTHOi'! nonS1pHoi1 CBR311. KoaaneHTHOCTb - 411cno 0611411x 3fl9KTPOHHblX nap. 3neKrpoorpu4arenbHOCTb (30) - cnoco6HocTb aToMa np11TS1r11eaTb CB060AHbl0 3fl0KTpOHbl (wKana n. no- n11Hra). 30 eo3pacrneT s nep110Ae. yMeHbwaeTCSI s rpyn ne. nep110A 30T lj N~°F(4,1) e- 30! Sc (0,86) Br X11Ml140CKaSI CBSl3b M0:>KAY 110HaMl1, ocy114ecTBnS1eMaS1 3a c4eT aneKTpocTa- Tl149CKoro npl1TSl:>K0Hl1SI , Ha3blBaeTCSI MOHHOM CBSl3bl0. 1916 r., 11A0SI KoccenSI K· + :;: ---+ K+ [:~: f 1,11 vi,v11 lllOHbl nepeXOA ne Na.+.~1:--+ Na+[:~1:r I I C111nb1 - (±)-0- np111H1>KeH111s:i --+_Ji-~- 1 I VIKP cpi1131114eCKllle CB-Ba: T T~n.l H20 p-p, pacnnaB 7 Ecn11 pa3HOCTb 3neKTpooTp114a- TenbHOCTei1 aTOMOB een11Ka, TO 3fl9K- TPOHHaSI napa, ocylljeCTBflRI01l4aS1 CBSl3b, nepeXOA11T K OAHOMY 113 aTOMOB, 11 o6a BaneHTHb1e 3neKTPOHbl MeTannoe AOCTaT04HO cna6o CBSl3aHbl co CBOMMM S1APaM11 11 MOryT nerKO OTpblBaTbCSI OT H11x. no3TOMY Mernnn c0Aep:>t<11r PSIA no- no:>t<11TenbHb1x 110HOB, pacnono:>KeHHblX B onpeAeneHHblX nono:>KeH11S1x Kp11cTann11- 4ecKoi1 peweTK11, 11 6onbwoe KOnl149CT- eo 3fl9KTpoHOB, CB060AHO nepeMeuta10- 1l411XCSI no BCeMy Kp"1CTanny. 3neKTpOHbl B Mernnne ocylljecTsnsi- IOT CBSl3b M0:>KAY BC0M"1 aTOMaMl1 MBTan- na. Me0 - ne --+Me"+ Me"++ ne --+ Me0 Cl>113M4 0CKMe CBOMCTB8 T (Hg - >K) 7 rnnno 6necK' KOBKOCTb Ocylljecrsns:iercS1 3a c4eT 3neKrpOHHOlil napb1, n p11H~e:>Kalljei1 o6o"1M aToMaM. Ecn11 aneKTPOHHaSI nnoTHOCTb pacnono:>t<eHa C"1 MM9Tpl14HO M0 :>KAY aTOMaM"1 , KOBaneHTHaSI CBR3b Ha3blBaeTCSI HenonsipHOM. Ecn"1 3neKrpo HHaS1 nnoTHOCTb cMe114eHa B CTOpoHy OAHOro 113 aTOMOB, TO KOBaneHTHaSI CBSl3b Ha3blBaeTCSI no11S1pHOM. HenonsipHasi: 30=30 no11S1pHaS1: 30> 30 Pa3n 114a10T o6 MeHHbli1 11 AOHOpHo- aK4enrop- Hbli1 Mexa H"13M o6pa30BaH"1SI KOBaneHTHOi1 CBSl311. 06MeHHb/H MexaHH3M Ka:>KAbli'I aTOM Aaer no OAHOMY HecnapeHHOMY 3fl0KTPOHY B 06Ujyl0 3neKTpOHHYIO napy: A-+ ·A-+ Ar;:;iA A·+ ·B--+ Ar;:;iB :r. + ·r: --+ :r : r: .. a·· .. •• --(XIX)- r-r :6 . + ·6:--+ :6 :: 6 : '* O=O " I I MKP -@- @- ~---+ I I :r: - @-@- ~ I I g:---+ <±3 <±3 ~ <±3 c .. ..H· +· r:--+H: r :a •• •• --o:::x::>- H-+H Cl>M31140CKl19 CBOMCTB8 T, >K, r T~.! H20? neTyY111e Ji I I AKP ~ -®-®- !::......< ()---+ I I CT T~n.l ~ -®-®- I I Cn, Sin, (Si02)n. SiC ,qoHOpHo-aK4enropH&1if MexaHH3M 0A11H aTOM (AOHOp) npeAOCTaBnSleT 3fl9K- Tp0HHYIO napy, a APYrolil arnM (aK4enrnp) npeAO- CTBn S1eT AflR 3TOi1 napbl CB060AHYIO op611Tanb: Ao7op A: +oB+--+ Ar;:;iB+ '--' I aK1..1emop NH +H+--+ [ ~ ]+li10H ·~ 01 H"~'H aMMOHli1s:l s H :QH .. "! .. HO:-+Al3 .+--:0H KOMnneKCHblM li10H (TeTparli1APOKCO- anIOMHaTaHli10H) l :OH BOAOPOAH8SI CBSl3b 3 TO CBSl3b M0:>KAY nonO:>K11TeflbHO 3apS1:>K0H- HblM aTOMOM BOAOPOAa OAHOi1 MOfl0KYflbl 11 OTp11- 4aTenbHO 3apS1:>t<eHHblM aroMOM APYroi1 Monet<y- nb1. BOAOPOAHas:i CBR3b "1Meer 4acrn4HO 3neKTpo- crnrn4ecK"1i1, 4acrn4HO AOHOpHo-aK4enropHbli1 xa- paKr ep. 8- 8 + Bo,qopo,qHafl CBR3b vt3o6paJKeHa TO'!KBMM H--+3 .. . H---+3 ..8- H--+ O: ... °"'H 8 + .. H --+O: °"'H PeaK4HH HOHHOro o6MeHa PeaK4uu pa3noJKeHvtR - peaK41111, e pe- 3ynbTaTe KOTOpblX "13 OAHOro BelljeCTBa o6- pa3ylOTCSI ABa 11n"1 HecKonbKO APYrHX ee- UjeGTB. 2CH4 _!; C 2H2t + 3H2t PeaK4uu coe11uHeHvtR - peaK41111, B pe- 3ynbTaTe KOTOpblX 113 ABYX 11n11 H0CKOflbKl1X ee114eCTB 06pa3yeTCSI OAHO HOBOe B9Uj9CTBO. 2Fe + 3Cl2 ...... 2FeCl3 PeaK4uu 3aMe1.14eHvtR - peaK4"111, npore- Kal0Ujl1e MB>KAY npoCTblM"1 "' cno:>KHblM"1 ee- Uj0CTBaM"1; np11 KOTOpblX aTOMbl npOCTOrO ee- Uj9CTBa 3aMelljalOT aTOMbl OAHOro "13 3ne- M9HTOB B CflQ)l(HOM B8Uj0CTBe. 2AgN03 + Fe ...... Fe(N03)2 + 2Ag ! PeaK4uu o6MeHa - peaK41111, npoTeKa10- Uj11e MB:>KAY ABYMR cno:>t<HblMl1 BelljecreaM11, np11 KOTOpblX "1X COCTaBHble 4acrn o6MeH"1Ba- IOTCSI MeCTaMl1. Fe2(S04)3 + 3BaCl2 ...... 3BaS04i + 2FeCl3 OKHCnHren&Ho-soccraHoBHTen&H&1e peaK4HH PeaK14vtvt pa3noJKeHvtR OKHt m'IT9 11b 10 2Hg0 ...... 2Hg + 02t BOCCT8HOBHT911b PeaK4uu coe1JvtHeHvtR 4Li + 0 2 ...... 2Li20 PeaK4Hu 3aMe1.14eHvtR Zn+ 2HCI ...... ZnCl2 + H2t TepMOXHMH'lecKHe peaK4HH 3K3orepMvt4ecKue - peaK4"111, npoTeKa- 10Uj11e c Bb1A0fl9 Hl10M rennOTbl. H2 + Cl2 =2HCI + 184,6 KA>K 3HIJOTBpMvt4eCKvte - peaK411"1, npoTeKa- IOUj110 c nornOUj0H"10M TennOTbl. 1 1 2 N2 + 202 = NO - 90,4 l<A>K Tennosoilr 3cfJ<jJBKT XVIMW-leCKOH peaK4vtvt 3TO KOfll140CTBO TennOTbl, Bb1A0flSllOUjei1cSI B pe3ynbTare peaK41111 . 06paTHMble H Heo6paTHM&le peaK4HH Heo6parvtMb1e peaK4uu - peaK41111, npo- TeKalOUjl1e AO KOH4a, T. e. AO nonHoro "13pac- XOAOBaH"1SI OAHOro 113 pearnpyl0Ujl1X ee- UjBCTB. Ag+ Cl -+ AgCI 06parvtMble peaK4uu - x11M"14BCK"1e pe- aK41111, nporeKalOUj"1e np11 AaHHblX ycno011S1x eo B3al1MHO nporneonono>KHblX HanpasneH11- S1X. V1HcjJOpMa4HOHHO-Cnpaao,HaR ra6nH4a ©000 «MH<Ponnacr., 2004 r. MocKaa, KaumpcKoe wocce, 21 E-mait mail@infop/ast ru Http:llwww.infop/astru Ten.: (095) 320-94-89 <PSKC: (095) 320- 94-88 not{m1C8HO B nelf8Tb 26.02.07. TMpa:« 4000 3K3. 3aK83 Ng 3497. "13,lfBTeflb 000 «MHcfJOnnBCT•, MOCKBB, KawMpCKOB WOCCe, 21. T111norp8c/JMR 000 «Bvtaa-Crap». 107023, MOCKBB, yn. 3neKTp038BOACKBR, 20.
  • 76.
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  • 77.
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  • 78.
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PeweHHe Mr (C02-3) =Ar (C) + 3 Ar (0) = 12,0 + (3·16,0) = 60,0 CneAOBarenbHO, M (C02-3) = 60,0 r/MOJlb 'IHcno 'laCTH1' seu.cecrsa MOJKHO BblYVICflVITb, eCJlVI Vl3BeCTHO KOJlVIYeCTBO AaHHOrO Bell.!eCTBa n B MOJ151X JlVl60 Macca AaHHOrO Bell.!eCTBa m B rpaMMax. ,iJ.Jl51 3TOro VICnOJlb3YIOT CfleAYIOLl.!ee Bblpa>KeHVle: N=n NA= (m/M)· ,.. -nOCT051HHaP. ABOraApO. npHMep 8blYVICJlVIM YVICJlO MOJleKYJl BOAbl H20 B 100 r BOAbl PeweHHe m(H20) 100 r N(H20) M(H20 ) ·NA= 18,0 r/MOflb ·(6,02·1023MOJlb-1)= 33,4 ·1023 CrexHoMerpH'leCKHe K03c/>c/>HL(HeHTbt- K03</J</J1111.1111eHTbl, CTORUl/lfe nepe.a </JOPMY118M/lf aeu.iecTB B ypasHeH/llRX peaKL(/11/11. 0HVI npeACTaBJ15llOT COOTHOWeHVl51 KOJlVIYeCTB VICXOAHblX Bell.!eCTB (B MOflb) VI npOAYKTOB peaKU,VIVI. HanpVIMep, CTeXVIOMeTpVIYeCKVle K03cpcpVIU,VleHTbl B ypaeHeHVIVI peaKU,VIVI nonyYeHVl51 npocToro cynnepcpoccpara Ca3(P04)2+2H2S04 ~Ca(H2P04)2+2CaS04 CBVIAeTeflbCTBYIOT, YTO Afl51 nonyYeHVl51 1 MOflb AVlrlllAPOcf>occpara KaflbU,Vl51 Ca(H2P04)2 HMO B351Tb 1 MOJlb cpoccpara KaflbU,V151 Ca3(P04)2 VI 2 MOJlb cepHOLli KVICJlOTbl H2S04. CrexHoMerpH'leCKHe HHAeKc&t - 3TO YVICJla, CT051Ll.!Vle B XVIMVIYeCKVIX cpopMynax cnpaBa BHVl3Y npVI CVIMBOflaX XVIMVIYeCKVIX 3JleMeHTOB. CTexV10MerpV1YeCKV1e VIHAeKCbl xapaKTepV13YIOT KOJlVIYeCTBeHHOe COAep)l(aHVle XVIMVIYeCKVIX 3fleMeHTOB B COeAVIHeHVl51X. HanpVIMep, VIHAeKCbl B cpopMyJle rVIApa3VIHa N2H4 noKa3blBalOT, YTO e MOJleKyne rV1Apa3V1Ha Ha 2 aTOMa a3oTa npVIXOAVITC51 4 aTOMa BOAOPOAa, a B 1 MOJlb MOJleKyfl rVIApa3VIHa Ha 2 MOflb aTOMOB a30Ta npVIXOAVITC51 4 MOJlb aTOMOB BOAOPOAa. 3aKOHbl CTeXMOMeTpMM. 3TOT 3aKOH OTKpblT VI 3KCnep111MeHTaJlbHO o6ocHoeaH M.B.noM0Hocoeb1M (1748), a 3aTeM cppaHU,Y3CKVIM XVIMVIKOM A.naeya3be (1789). 3TOT 3aKOH rnaCVIT: .- nocne OTKpblTVl51 A.3HWTeiliHOM B 1905 r. B3aVIMOCB513VI Me>KAY Maccoili VI 3Heprvieili, KOTOpa51 BblpaJKaeTC51 ypaBHeHVleM E=mc2 rAe E-<1HeprV15I; m-Macca; c-cKopocTb ceera e eaKyyMe, 6b1Jl ccpopMyllVIPOBaH 6onee 06°Ll.!Vlili
  • 79.
    0THOWeH"1e M ccK"1CnopoAa"' 330Ta B OKC"1A3X'a30ilia. 0KCHAa30Ta N20 NO N203 N204 N205 3aKOH <t>opMy11111pyeTCR o6pa30M: CyMMa Maccbl seutecTsa CHCTeMbl ,,, MaCCbl, KOTOpafl 3KBHBaneHTHB 3HeprHH, nOR}"leHHOH HnH OT,QBHHOH TOH JICe CHCTeMOH, nOCTOflHHa. 3TOT 38KOH 6bl11 ycTaHos11eH A>K. AanbTOHOM e 1803 r. ECJIH ABB 3/leMeHTa 06pa3y10T Me)l(,O,y co6oii 6onee op,Horo COeP.HHeHHfl, TO MaCCtJ QQHOro 3neMeHTa, npHXOP.flutHeCSI Ha OP.HY H TY JKe Macey p,pyroro 3/leMeHTa OTHOCflTCfl Me)l(,O,y co6oif KaK He6onbWHe Lie/Ible 'IHcna. AeiAcTe111e :noro 38KOH8 MO>KHO npo111111110CTPMPOB8Tb H8 rtpM~ OKCMAOB 830T8. 3TOT 38KOH c<t>opMy11111posan B 1808 r. )I(. npycT. Ka)l(,O,oe XHMH'l8CK08 He3aBHCMMO OT cnoco6a ero non}"leH/lffl COCTOHT H3 OIJ.HHX H Tex JIC8 3J18MeHTOB, npwleM OTHOIUeHWI Hx Mace nocTOJtHHbl, a OTHOCMT8RttHt.16 KOJlH'leCTBa HX BTOMOB BblpaJICS/OTCSI l.f6/lblMH 'IHCJIBMH. 38KOHbl AaJibTOH8 111 npyCT8 cnpaB9,D,11111Bbl TOl1bKO A/lSI >KMAKMX .., ra3006pa3HblX CC>eAlllHeHMM c ra3006pa3HOM CTPYKTYPOM (Hanp!>1Mep, S02. S03, NH3, C5H5). TaKMe coeA111HeH111R e naMRTb A>K. Aa11bTOHa Ha3B8Hbl A8l1bTOH111AaM111. HapRAY c A8l1bTOHlllA8Mlll cyU.(eCTBYIOT HeCTeXlllOMeTpMYeCKllle C08AlllHeHMR- 6epTOl1111Abl. 6epTOm'IAbl-KPlllCTann111YecK111e <t>a3bl nepeMeHHOro COCT8B8, B KOTOPblX OTHOW8HlllR KOl1111Y8CTB p83HOPOAHblX 8TOMOB He MOryT 6b1Tb TOYHO Bblpa>KeHbl M8l1blMlll ue11blMlll YlllCl18Mlll. Crnx1110MeTp111yecK111e lllHAeKCbl e <t>opMy11ax 6epTOl1l1111AOB MOryT 6b1Tb Heue110YMCl1eHHblMM. 6epTOl1l1111Abl Y8CTO BCTpeYSIOTCR Cp&AM &ttt8pHblX CQeAMHeHMM Macca KHcnopoAa, npHXOAS1~aS1CS1 Ha 1 r a3oTa (1·16): (2· 14) =0,5714 (1·16): (1·14) =1,1428 (3•16): (2·14) =1,7143 (4·16): (2·14) =2,2857 (5·16): (2·14) =2,8571 cy11b<t>11tAOB T.n .) MaCCbl pearnpylOUIHX se11.1eCTB OTHOCflTCfl Me)l(,O,y co6oif KBK MOllflPHble MaCCbl HX 3KBHB8/leHTOB. 3KBlllB8neHT - 3TO peanbHQR 11111111 YCl10BH8SI eAlllHlllU8 BeU.(eCTBa, KOTOpaR B A8HHOM K111Cl10THO OCHOBHOl-1 peaKUllllll 3KBMB8neHTH8 OAHOMY K8TlllOHY BOAOPOA8 111n111 B A8HHOM OKlllCl1111T8l1bHO-BOCCT8HOBMT0l1bHOM peaKUllllll OAHOMY 3l1eKTPOHy. ct>aKTOp 3KBlllB8l10HTHOCTll1 YMCno, 0603H8Y8IOU.(ee, K8K8R AOl1R pea11bHOM YacT111~ eeU.(ecTea 3Ks111saneHTHa OAHOMY K8TlllOHY BOAOPOA8 B A8HHOl.1 K111Cl10THO- OCHOBHOM peaKUllllll 11111111 OAHOMY 3l1eKTpOHY B A8HHOM OKlllCl1111Tel1bHO-BOCCT8HOBlllTel1b- peaKU111111 . 3TO 6eapaaMepHasi B K111cnoTHo-ocHoBHOlii peaKu111111 Me>K,D,y cepOBOAOPOAOM .., rMAPOKClllAOM H8TPlllR, B3RTOM B 11136blTKe, H2S + 2NaOH = Na2S + 2H20 yYacTeyioT o6a KaTMOHa BOAOPOAa Ka>K,D,oi:.1 Mo11eKY11bl ceposoAOPOAa. B 3TOM Cl1yYae OAHOMY KQTl/IOHY w 3KBMBBn0HTHa yc11oeHaR YaCTMUa-1/2 Mo11eKynbl H2S, a faKe (H2S) = 1/2. Ec11111 >Ke cepoeOAOpoA 111 rlllAPOKClllA HSTPMR B3RTbl B T8KlllX COOTHOWeHMRX, YTO B P83Yl1bT8Te peaKUlllM o6paayeTCR r11tAPO- cy11b<t>aT H8TPMR H2S + NaOH = NaHS + H20 TO B K8)1(,ll,OH MOl1eKYl1e cepOBOAOPOA8 38M0U.80TCR TOl1bKO OAlllH K8TMOH BOAOPOAQ. B 3TOM c11yYae OAHOMY 1110Hy W 3KBMBaneHTH8 peal1bH8R MOn0KYJ18 H2S Ill f3 Ke (H2S) = 1 . Yacrnua- Ko111i1yecTeo 3Ke111ea11eHTa M3MepsieTCR e MOl1RX, KBK.., l1I06oe KOl1MY0CTBO B0U.0CTB8. Macca 1 MOl1b 3Ke111eaneHTa , r.e. MonRpHaR Macca 3KBlllB8n8HT8, paeHa npo113BeAeHMIO 0THOW9HHe Mace KHCnopoAa,npHXOASl~HXCSI Ha 1 r a3oTa, K0,5714 (Toit'JKe senH'IHHe .ctnR N20) 1 2 3 4 5 <t>aKTOpa 3KBMB8n8HTHOCTM Ha MOl1RPHYIO Macey seU.(ecTBa. Hanp111Mep, MOl1RpHaR Macca 3KB111ea11eHTa cepoBOAOPOAa B KMCl10THO-OCHOBHOM peaKUMM c M36blTKOM rMAPOKCMAa H8TpMR M(1/2 H2S)= a f3Ke (H2S) ·M(H2S) B paBHblX o6beMax pa3/IH'IHblX ra30B npH OP,HHaKOBblX TeMnepaT}'pax "' .o.asneHHH co.o.ep)l(HTbCfl 0P,HH8KOBOe 'IHC/10 MOlleKyll. l-13 3aKoHa AsorQAPo cneAyeT, YTO: *1) np111 HOPMBnbHOM Aae11eH111111 (101,3 Kna=1 aTM) .., TeMnepaType o0 c 1 MOl1b ' mo6orc ra3a 3aHMMaeT o6'beM 22,4 n; *2) nJlOTHOCTM AByx raaoe npM OAHMX .., Tex *e A8Bl10HMM 111 TeMnepaType npRMO nponopuMOH8nbHbl MX MOl1RPHblM M8CC8M. 3TOT 38KOH 6bln OTKPblT B 1808 r. )I(, n.relii- l'lpH nocTOJtHHOM .o.asneHHH ,,, TeMneparype OIMMW pearnpy1011.1Hx Me)l(,O,y co6oif npQA)'tC108 peSKl.llAH OTHOCflTCfl KSK Het1onbWHe "811bl8 'IHC/llJ. I4607061 652306 MH<l>opM&l4MOHHO· cnpaao'IH&R Tal511M14a 000 "lllHQ>onnacr", 2006 r. MocKea, Kaw111pcKoe wocce, 21 e-mail: mail@infoplast.ru, http://www.infoplast.ru TBJI., (495) 320-94-89/88