After watching this ppt you will get answers of the questions like...
1) What does it mean?
2) What we study in calculus?
3) Who invented it?
4) What was the need to invent it?
and many more...
You will also learn about the basic difference between discrete and continuous.
And many real life and cool applications of calculus....
This Presentation Is Specially Made For Those Engineering Students Who are In Gujarat Technological University. This Presentation Clears Your All Doubts About Basics Fundamentals of Numerical Integration. Also You Will Learn Different Types Of Error Formula To Solve the Numerical Integration Sum.
Explain the relationships between corresponding parts of the pre-image and image of a dilation.
Creating an image by enlarging or reducing a figure is called adilation .
The image is the figure resulting from the dilation.
The preimage is the original figure.
The pre-image and image are similar figures.
You can examine the corresponding vertices and corresponding sides to describe a relationship between the pre-image and image of a dilation.
After watching this ppt you will get answers of the questions like...
1) What does it mean?
2) What we study in calculus?
3) Who invented it?
4) What was the need to invent it?
and many more...
You will also learn about the basic difference between discrete and continuous.
And many real life and cool applications of calculus....
This Presentation Is Specially Made For Those Engineering Students Who are In Gujarat Technological University. This Presentation Clears Your All Doubts About Basics Fundamentals of Numerical Integration. Also You Will Learn Different Types Of Error Formula To Solve the Numerical Integration Sum.
Explain the relationships between corresponding parts of the pre-image and image of a dilation.
Creating an image by enlarging or reducing a figure is called adilation .
The image is the figure resulting from the dilation.
The preimage is the original figure.
The pre-image and image are similar figures.
You can examine the corresponding vertices and corresponding sides to describe a relationship between the pre-image and image of a dilation.
Arrebatamento - Entrevista Com Apóstolo Sérgio Octávio Félix
Entendendo o Arrebatamento, os sinais da volta de Jesus e a última semana de Daniel, os 7 anos.
A Volta de Jesus e os Sinais do Fim dos Tempos.
Apocalipse e os Acontecimentos finais que antecedem a vinda de jesus
Sinais dos últimos dias e a volta de jesus.
Quando acontecerá o Arrebatamento?
Por que o arrebatamento ainda não aconteceu.
Quando tempo ainda até a volta de Jesus.
Que sinais ainda tem que se cumprir.
В статье представлен общий обзор технологии лазерного сканирования
объектов в пространстве, рассмотрены устройства, реализующие
эту технологию и применяющиеся в мобильных робототехнических
комплексах.
Ο Ανοιχτός Καταπιστευτικός Λογαριασμός είναι ένας μηχανισμός που εξασφαλίζει στους δικαιούχους προγραμμάτων ΕΣΠΑ πρόσβαση σε ποσό ίσο με την προκαταβολή που δικαιούνται, χωρίς να απαιτείται η υποβολή εγγυητικής επιστολής.
Η σύσταση του Ανοιχτού Καταπιστευτικού Λογαριασμού στο Ταμείο Παρακαταθηκών και Δανείων σχεδιάστηκε με σκοπό την ενίσχυση της ρευστότητας της αγοράς και τη διευκόλυνση των Δικαιούχων. Οι όροι, οι προϋποθέσεις και κάθε αναγκαία λεπτομέρεια για τη σύσταση του Λογαριασμού στο Ταμείο ορίστηκαν με την υπ’ αριθμό 62550/2016 Απόφαση του Υφυπουργού Οικονομίας, Ανάπτυξης και Τουρισμού (ΦΕΚ Β 1738).
Η χρήση του Εscrow Αccount από τους Δικαιούχους κρατικών ενισχύσεων δεν είναι υποχρεωτική. Ο κάθε Δικαιούχος δύναται είτε να αξιοποιήσει τον Ανοιχτό Καταπιστευτικό Λογαριασμό, είτε να ακολουθήσει την παραδοσιακή διαδικασία λήψης της προκαταβολής ή και καταβολής της επιχορήγησης.
Άνοιγμα λογαριασμού και εκταμίευση της χρηματοδότησης σε 3 βήματα
Βήμα 1: Με την υπογραφή της εγκριτικής απόφασης υπαγωγής ενός Δικαιούχου σε χρηματοδοτικό πρόγραμμα, ενεργοποιούνται και οι διαδικασίες χρήσης του Εscrow Αccount. Ειδικότερα, μετά από αίτημα του επενδυτή/Δικαιούχου, στο οποίο θα δηλώνει τη βούλησή του για χρήση του escrow και τη δήλωση προσχώρησης στη σύμβαση, δημιουργείται στον Εscrow Αccount, που αφορά τη δράση στην οποία έχει ενταχθεί, υπο-λογαριασμός/μερίδα στο όνομά του.
Βήμα 2: Για την αποδέσμευση της χρηματοδότησης, ο Δικαιούχος, αφού πρώτα έχει ολοκληρώσει ένα μέρος του επενδυτικού σχεδίου (καθορίζεται από τον εκάστοτε Οδηγό Εφαρμογής του χρηματοδοτικού προγράμματος), θα πρέπει να υποβάλλει στο Πληροφοριακό Σύστημα Κρατικών Ενισχύσεων (ΠΣΚΕ) αίτημα επαλήθευσης - καταβολής των δαπανών του, συνυποβάλλοντας τα μερικώς εξοφλημένα τιμολόγια και τυχόν ποσοστό ιδιωτικής συμμετοχής. Το μη εξοφλημένο ποσό των τιμολογίων θα καταβληθεί στη συνέχεια από τον Ανοικτό Καταπιστευτικό Λογαριασμό.
Όσον αφορά τις Δράσεις στις οποίες το ύψος της επιδότησης ανέρχεται στο 100% ("Νεοφυής Επιχειρηματικότητα", "Ενίσχυση της Αυτοαπασχόλησης Πτυχιούχων Τριτοβάθμιας Εκπαίδευσης"), τα τιμολόγια θα είναι μερικώς εξοφλημένα ως προς τη μη επιλέξιμη δαπάνη (π.χ. ΦΠΑ). Σε κάθε περίπτωση, ο Δικαιούχος θα πρέπει να έχει ασφαλιστική και φορολογική ενημερότητα.
Βήμα 3: Μετά από έλεγχο των προσκομισθέντων δικαιολογητικών από τον Ενδιάμεσο Φορέα Διαχείρισης - ΕΦΕΠΑΕ, δίνεται εντολή στο Ταμείο να αποδεσμεύσει - εκταμιεύσει από τον λογαριασμό του Δικαιούχου συγκεκριμένο ποσό υπέρ κάθε παρόχου - προμηθευτή του Δικαιούχου για λογαριασμό του και μέχρι το ανώτατο ύψος της δημόσιας δαπάνης. Τα χρήματα, δηλαδή, δεν πιστώνονται στον Δικαιούχο, αλλά απ' ευθείας στους προμηθευτές του.
Στη συνέχεια, η εντολή αποστέλλεται σε ηλεκτρονική μορφή ψηφιακά υπογεγραμμένη από τον ΕΦΕΠΑΕ στο Ταμείο, που εκτελεί τις πληρωμές, καταβάλλοντας άμεσα τα σχετικά ποσά στους λογαριασμούς, που τηρούν οι πάροχοι - προμηθευτές του Δικαιούχου σε πιστωτικά ιδρύματα.
Έντυπο Υποβολής για το πρόγραμμα της ενίσχυσης έως 50%, έως €200.000, υφιστάμενων πολύ μικρών και μικρών επιχειρήσεων μέσω της ανάπτυξης των ικανοτήτων τους στις νέες αγορές και που δραστηριοποιούνται στους τομείς της αγροδιατροφής & βιομηχανίας τροφίμων, των πολιτιστικών & δημιουργικών βιομηχανιών, των υλικών & των κατασκευών, της εφοδιαστικής αλυσίδας, της ενέργειας, του περιβάλλοντος, των τεχνολογιών πληροφορικής & επικοινωνιών και της υγείας. Πληροφορίες: info@wintowin.gr, 2103608609
Δημοσιεύθηκε το πρόγραμμα Νεοφυής Επιχειρηματικότητα 2016. Αφορά ίδρυση μικρών και πολύ μικρών επιχειρήσεων από άνεργους ή αυτοαπασχολούμενος με έμφαση σε καινοτόμα επιχειρηματικά σχέδια και στην ενίσχυση της απασχόλησης με τη δημιουργία βιώσιμων νέων θέσεων απασχόλησης. Πληροφορίες: info@wintowin.gr, 2103608609
Presentation at the Bernadotte Academy in 2007 by Infosphere CEO Mats Björe about the concept of OSINT. Examples from tools like Silobreake is included
Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
3. PRE REQUISITE KNOWLEDGE
Coordinate geometry
Locus
Congruency and Similarity
Vectors
Angle measure
matrices
4. DEFINITION
Transformation is a Geometrical operation that maps
/shifts/moves a set of point(s) (objects) from one position to
another position (image) following certain specified set of
rule(s).
TYPES OF TRANSFORMATIONS
Basically there are six types of Transformations namely
1. Translation (T)
2. Reflection (M)
3. Rotation (R)
4. Enlargement (E)
5. Shear (H)
6. Stretch (S)
Congruencies/Isometries
Affines
Similarity
TRANSFORMATIONS
5. 1. TRANSLATION ( T )
In a Translation,
1. The object and the image have exactly the same size and
shape. (congruent).
2. The object and the image face the same direction.
A Translation is fully described by a column vector / translation
vector. x
y
It is important to be aware of the positive and negative vector
components of the translation.
Objectives: Identify and name a translation.
Calculate the column Vector
Describing the translation fully.
Calculate coordinates and draw the image or the object on
the Cartesian plane.
6. ACTIVITY 1
(a) Triangle A has coordinates (1, 1), (4, 1) and (1, 2) and Triangle B
has Vertices (3, 4), (6, 4) and (3, 5). Draw and label the
Triangles A and B clearly.
(b) Name the transformation that maps ∆ A onto ∆ B
(c) ∆ A is mapped onto ∆ C by a translation. Write down its column
vector.
(d) ∆ A is mapped onto ∆ D by a translation whose column vector is
- 5
2 Calculate the coordinates of ∆ D, hence draw and label ∆ D
clearly.
(e) Describe fully the single transformation that maps ∆ D onto ∆ B
8. SOLUTION
(a) On the graph
(b) Translation
(c) Column Vector = Image coordinate – Object coordinate.
Column Vector = 0 - 4 = -4
-4 1 -5
(d) -6 = x - 1
2 y 1 ( x , y ) = (- 4, 3 )
(e) ∆ D onto ∆ B by a translation whose column vector is 7
1
9. 2. REFLECTION (M)
In a Reflection,
1. The object and the image have exactly the same size and shape.
(congruent).
2. The object and the image face the exact opposite direction.
3. A refection is fully described by the equation of the mirror line ( Usually
drawn as a dotted line)
4. The mirror line is the perpendicular bisector of the two corresponding
points ( from the Object and the Image)
Objectives: - Identify and name a reflection.
- Calculate the equation and draw the mirror line.
- Describe the reflection fully.
- Calculate coordinates and draw the image or the object on the
Cartesian plane.
Introduction of matrices for reflection in the x-axis and the y-axis.
10. ACTIVITY 2
(i) Name the transformation that maps triangle ∆ABC onto triangle
∆ A1B1C1.
(ii) ∆ ABC is reflected onto ∆A2B2C2 by a reflection in the y-axis.
Draw and label ∆A2B2C2.
(iii) ∆A2B2C2 is reflected onto ∆A3B3C3 in the line M. Draw, label
and write down the equation of line M.
(iv) ∆ABC is reflected onto ∆A4B4C4 in the line y = x. Draw and
label ∆A4B4C4
(v) Name the transformation that maps ∆ABC onto ∆A3B3C3.
(vi) Name the transformation that maps ∆A4B4C4 onto ∆A2B2C2.
12. 3. ROTATION (R)
In a Rotation,
1. The object and the image have exactly the same size and shape.
(congruent).
2. The direction of object and the image is neither the same nor direct
opposite.
A Rotation is fully described by the direction, angle and Centre of rotation
Objectives: - Identify and name a rotation.
- Find the centre by construction and measure the angle of
rotation Clockwise or anticlockwise.
- Describe the rotation fully.
- Calculate coordinates and draw the image
or the object on the Cartesian plane.
The angles matrices must include +90, 180 and - 90. centre (0, 0)
14. MATRICES REPRESENTING ROTATION ABOUT (0,0)
The Matrix 0 -1 represents an anticlockwise rotation of 90
1 0 about ( 0, 0 )
The Matrix -1 0 represents an anticlockwise rotation of 180
0 -1 about ( 0, 0 )
The Matrix 0 1 represents an clockwise rotation of 90
-1 0 about ( 0, 0 )
15. ACTIVITY 3
(i) ∆ABC is mapped onto ∆ PQR by an anticlockwise rotation of 90 Degrees.
Find the centre of rotation.
(ii) ∆ ABC is mapped onto ∆A1B1C1 by a clockwise rotation of 90 about (0,0).
Draw and label ∆A1B1C1.
(iii) ∆PQR is mapped onto ∆P1Q1R by a clockwise rotation of 90. Draw and label
∆P1Q1R.
(iv) Name the transformation that maps ∆ABC onto ∆P1Q1R.
(v) ∆P1Q1R. Is translated onto ∆A2B2C2 by a column vector 2
Draw and label clearly ∆A2B2C2. - 6
(i) Describe fully the transformation that maps ∆A2B2C2 onto ∆A1B1C1.
16.
17. ACTIVITY 4
Describe fully the transformation that maps
(i) ABCD onto PQRS
(ii) ABCD onto QPSR
(iii) ABCD onto RSPQ
(iv) ABCD onto SPQR
18. SOLUTIONS TO ACTIVITY 4
(i) Translation
Column Vector = 4
0
(ii) Reflection
y-axis (x = 0 ) as the mirror line.
(iii) Rotation of 180 degrees.
Centre ( 0, 0 )
(iv) Clockwise rotation of 90 Degrees.
Centre ( 0, -2)
19. 3. ENLARGEMENT (E)
In an Enlargement,
1. The object and the image are Similar i.e. corresponding sides are in
the same ratio.
2. The direction of object and the image can either be the same or
opposite.
An Enlargement is fully described by the centre and Scale factor
Objectives: - Identify and name an Enlargement.
- Find the Scale factor of an Enlargement
- Find the centre of enlargement
- Recall the matrix for enlargement Centre (0,0) and apply it
to find the coordinates of the Image or object.
The matrix k 0 represents an enlargement centre (0,0) and Scale factor k
0 k
20. ACTIVITY 5
(a) Draw x and y axes for – 8 ≤ x ≤ 8 and – 8 ≤ y ≤ 8
(b) Draw and clearly label ∆ABC for which A(2,1), B(2,4) and C(1,4)
(c) ∆ABC is mapped onto ∆A1B1C1 by a matrix 2 0
0 2
(d) Describe fully the Transformation that maps ∆ABC onto
∆A1B1C1
(e) ∆ABC is mapped onto ∆A2B2C2 by an Enlargement centre (0,0)
and scale factor – 2.
(f) ∆ABC is mapped onto ∆A3B3C3 by an Enlargement. Find the
centre of enlargement and the scale factor.
(g) Describe fully the transformation that maps ∆A2B2C2 onto
∆A3B3C3.
21.
22. SHEAR (H)
In a shear the Object is sheared onto the Image with its area and perpendicular
height maintained.
In a Shear the movements of the points is parallel to the invariant line.
A shear is fully described by the equation of the invariant line and the shear
factor ( ± k ).
Objectives: - Identify and name a Shear.
- Find the Shear factor and the equation of the Invariant line.
- Recall the matrix for Shear x-axis / y-axis as the invariant
line and use it to find the coordinates of the Image or object.
The matrix 1 k represents a shear x-axis as the invariant and Shear factor k
0 1
The matrix 1 0 represents a shear y-axis as the invariant and Shear factor k
k 1
23. .
ABCD is mapped onto ABC1D1 by a shear.
Line AB is the invariant and Shear Factor = DD1
AD (positive shear factor)
ABCD is mapped onto ABC2D2 by a shear.
Line AB is the invariant and Shear Factor = DD2
AD (Negative shear factor)
25. 6. STRETCH (S)
A Stretch is an Enlargement in one direction.
In a stretch the movement of points is perpendicular to the Invariant line.
A stretch is fully described by the equation of the invariant line and the Stretch
factor ( ± k )
Objectives:- Identify and name a Stretch.
- Find the Stretch factor and equation of the Invariant line.
- Recall the matrix for Stretch x-axis/ y-axis as the invariant line and
use it to find the coordinates of the Image or object.
The matrix 1 0 represents a stretch x-axis as the invariant and Shear factor k
0 k
The matrix k 0 represents a stretch y-axis as the invariant and Shear factor k
0 1