Fermat's Little Theorem states that if p is a prime and a does not divide p, then a^p-1 is congruent to 1 modulo p. Using this, we can reduce exponents modulo p. Here, 7 is prime and 3 does not divide 7, so 3^6 is congruent to 1 modulo 7. Since 999999999 = 16666666*6 + 3, we can reduce the exponent to get 3^999999999 is congruent to 3^3, which is congruent to 6 modulo 7.
The document provides an agenda for an English lesson about transportation. It includes discussing means of transport, the present simple tense and its use for future events, a listening activity with questions about transport, and homework assignments from the textbook. Students are asked to label types of transportation, fill out a chart by asking each other questions, and complete exercises for homework. The lesson aims to teach vocabulary and grammar related to discussing travel plans.
This document outlines a microteaching activity for secondary school students that involves discussing pictures of important places in San Francisco, performing speaking exercises using prepositions and realia materials, and creating role-plays in small groups using flashcards. The activity aims to demonstrate how authentic materials can be used in the English classroom to motivate students and support their English language acquisition.
The document outlines several rules of composition in photography: simplicity focuses the viewer on the subject by removing background distractions; the rule of thirds divides the frame into thirds for subject placement; lines change the angle or viewpoint to see more detail; balance uses objects or colors to evenly distribute visual weight; framing focuses on the center of interest; and avoiding mergers prevents other elements from detracting attention from the main subject.
Organization design is like teen romance in that it requires both creativity and execution to drive innovation. Effective organization design can disrupt existing business models and introduce radical new technologies, products, and processes, similar to the excitement and uncertainty of a new summer fling. However, organization design also involves incremental improvements through style adjustments and line extensions, just as mature relationships develop over time through adaptation and understanding. Ultimately, organization design and romance both require balancing bold vision with practical implementation to achieve meaningful change.
Fermat's Little Theorem states that if p is a prime and a does not divide p, then a^p-1 is congruent to 1 modulo p. Using this, we can reduce exponents modulo p. Here, 7 is prime and 3 does not divide 7, so 3^6 is congruent to 1 modulo 7. Since 999999999 = 16666666*6 + 3, we can reduce the exponent to get 3^999999999 is congruent to 3^3, which is congruent to 6 modulo 7.
The document provides an agenda for an English lesson about transportation. It includes discussing means of transport, the present simple tense and its use for future events, a listening activity with questions about transport, and homework assignments from the textbook. Students are asked to label types of transportation, fill out a chart by asking each other questions, and complete exercises for homework. The lesson aims to teach vocabulary and grammar related to discussing travel plans.
This document outlines a microteaching activity for secondary school students that involves discussing pictures of important places in San Francisco, performing speaking exercises using prepositions and realia materials, and creating role-plays in small groups using flashcards. The activity aims to demonstrate how authentic materials can be used in the English classroom to motivate students and support their English language acquisition.
The document outlines several rules of composition in photography: simplicity focuses the viewer on the subject by removing background distractions; the rule of thirds divides the frame into thirds for subject placement; lines change the angle or viewpoint to see more detail; balance uses objects or colors to evenly distribute visual weight; framing focuses on the center of interest; and avoiding mergers prevents other elements from detracting attention from the main subject.
Organization design is like teen romance in that it requires both creativity and execution to drive innovation. Effective organization design can disrupt existing business models and introduce radical new technologies, products, and processes, similar to the excitement and uncertainty of a new summer fling. However, organization design also involves incremental improvements through style adjustments and line extensions, just as mature relationships develop over time through adaptation and understanding. Ultimately, organization design and romance both require balancing bold vision with practical implementation to achieve meaningful change.
The document provides information about various news organizations like the BBC and CNN, and topics such as earthquakes, sports, architecture, art and science. The BBC is the world's largest broadcasting organization headquartered in London, producing radio and television output daily through foreign bureaus. Deutsche Welle is a German public broadcaster headquartered in Berlin that broadcasts in 30 languages. The document also mentions topics like tidal waves, earthquakes, football, basketball, painting, sculpture, and scientific investigation.
This document outlines a microteaching activity for secondary school students that involves discussing pictures of important places in San Francisco, performing speaking exercises using prepositions and realia materials, and creating role-plays in small groups using flashcards. The activity aims to demonstrate how authentic materials can be used in the English classroom to motivate students and support their English language acquisition.
This short document provides basic personal details about the author, including that they are a 15 year old male who lives in Columbus, Ohio and is a 9th grader. It touches on their interests and what they want to do in the future, as well as people they respect, but does not provide specifics. The author concludes by thanking the reader for learning about them.
This document contains 95 mission statements from various non-profit organizations covering a wide range of causes including environmental conservation, human rights, healthcare, education, poverty alleviation, and animal welfare. The missions focus on goals such as ending hunger, curing diseases, protecting wildlife, providing assistance dogs, and advocating for civil liberties. They demonstrate the diverse ways that non-profits work to create positive change in local communities and globally.
The document appears to be notes from an English lesson about transportation vocabulary and the phrase "go by". It includes pictures of different vehicles like a plane, bus, boat, train, and more. It then provides examples of sentences using "go by" like "I go by boat" and "He goes by car". The second half discusses a conversation between Linda and Tom about their travel plans, where they will go by boat, coach, and plane to locations like France, Germany, Mongolia, and China. It emphasizes learning the new vocabulary and grammar to be able to discuss transportation and travel.
The folk song describes birds flying over mountains and singing songs that carry high above, listening to the voice of the singer's beloved. It asks the beloved to sing their song and fly around the singer's heart with the birds, and to please come again like the migrating birds that fly across the sky to the horizon.
The document provides information about various news organizations like the BBC and CNN, and topics such as earthquakes, sports, architecture, art and science. The BBC is the world's largest broadcasting organization headquartered in London, producing radio and television output daily through foreign bureaus. Deutsche Welle is a German public broadcaster headquartered in Berlin that broadcasts in 30 languages. The document also mentions topics like tidal waves, earthquakes, football, basketball, painting, sculpture, and scientific investigation.
This document outlines a microteaching activity for secondary school students that involves discussing pictures of important places in San Francisco, performing speaking exercises using prepositions and realia materials, and creating role-plays in small groups using flashcards. The activity aims to demonstrate how authentic materials can be used in the English classroom to motivate students and support their English language acquisition.
This short document provides basic personal details about the author, including that they are a 15 year old male who lives in Columbus, Ohio and is a 9th grader. It touches on their interests and what they want to do in the future, as well as people they respect, but does not provide specifics. The author concludes by thanking the reader for learning about them.
This document contains 95 mission statements from various non-profit organizations covering a wide range of causes including environmental conservation, human rights, healthcare, education, poverty alleviation, and animal welfare. The missions focus on goals such as ending hunger, curing diseases, protecting wildlife, providing assistance dogs, and advocating for civil liberties. They demonstrate the diverse ways that non-profits work to create positive change in local communities and globally.
The document appears to be notes from an English lesson about transportation vocabulary and the phrase "go by". It includes pictures of different vehicles like a plane, bus, boat, train, and more. It then provides examples of sentences using "go by" like "I go by boat" and "He goes by car". The second half discusses a conversation between Linda and Tom about their travel plans, where they will go by boat, coach, and plane to locations like France, Germany, Mongolia, and China. It emphasizes learning the new vocabulary and grammar to be able to discuss transportation and travel.
The folk song describes birds flying over mountains and singing songs that carry high above, listening to the voice of the singer's beloved. It asks the beloved to sing their song and fly around the singer's heart with the birds, and to please come again like the migrating birds that fly across the sky to the horizon.
The document outlines an English lesson plan about shopping. The lesson aims to teach students how to use this/that and these/those when referring to objects. The plan includes warm-up activities, an exercise matching items to stores, practicing store names, and a grammar lesson on one/ones and this/that/these/those. Students will then complete sentences using the new vocabulary and review by answering questions about purchases made in the story dialogue. For homework, students finish the dialogue using words from a provided list.