real numbers‚ and a2 + b2 0. Prove that A is a group under matrix multiplication. (10) (b) Show that the set: M = forms a group under matrix multiplication. (5) (c) Can M have a subgroup of order 3? Justify your answer. (2) (Total 17 marks) 3. (a) Define an isomorphism between two groups (G‚ o) and (H‚ •). (2) (b) Let e and e be the identity elements of groups G and H respectively. Let f be an isomorphism between these two groups. Prove that f(e) = e. (4) (c) Prove
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sketch above to show triangle ABP.(b)Calculate the length of AP. 12. [pic] (a)Calculate the distance‚ OM‚ of the boy from the balloon. (b)Calculate angle MON. 13. In a triangle PQR‚ PQ = 12cm‚ QR = 1cm and PR = 13cm. Check whether this is a right triangle or not. 14.AD is a diameter of the circle
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one of the major contributions Canada made was the Royal Canadian Air Force. A significant contribution the air force made was they provided a place for allied pilots to train and supplied a large amount of money. The Air Force helped protect the convoys going across the Atlantic and helped develop new anti- naval weapons. Another contribution was defending Britain from German bombings and bombing Germany. For all these reasons‚ the RCAF made a very significant contribution to the victory of World
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Beyond Rivalry By Elizabeth Stark Psychology Today During childhood‚ sisters and brothers are a major part of each other’s lives‚ for better or for worse. As adults they may drift apart as they become involved in their own careers‚ marriages and families. But in later life‚ with retirement‚ an empty nest‚ and parents and sometimes spouses gone‚ brothers and sisters often turn back to each other for a special affinity and link to the past. “In the stressful‚ fast- paced world we live in‚ the sibling
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Punctuality Punctuality is a very important part of military life for several reasons. one reason is that if someone is late for a patrol or convoy that patrol or convoy might haveto leave without that person. Another reason is because it will make whoever your relieving have to stay at work for longer than they are supposed to‚ tired and sluggish because of that fact‚ giving a high chance that whatever work that person does would be sub par and not up to standards because of lack of sleep.
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Vectors in Two and Three Dimensions Print References 1. H2 Mathematics for ‘A’ Level Volume 1‚ Federick Ho‚ David Khor‚ Yui-P’ng Lam‚ B.S. Ong 2. Core Maths for Advanced Level (2000)‚ L. Bostock & S. Chandler. 3. Pure Mathematics (2000)‚ A. Martin‚ K. Brown‚ P. Rigby‚ S. Riley. Non Print References 1. http://www.geocities.com/h2maths Objective: At the end of the chapter‚ students should be able to 1. understand the geometrical and physical interpretations of two and three dimensional
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INTRODUCTION Absenteeism is an important system of maladjustment. It is an isolated phenomenon but an integral part of psychology and economy of industrial production. It is a great social problem of great complexity born out of attitude‚ circumstances and compulsions‚ absentee forms a major problem in any factor because it directly affect in the loss of Monday and as a result the turnover too. All human beings are dynamic ever growing and learning because people may have sensible
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Name:__________________________ House:_________________________ Teacher: Tick the box against your class and teacher(s): Mr. Bowen Mr. O’Hara Unit 3 Physics Trial Exam Semester 1‚ 2013 Reading Time: 15 minutes Examination Time: 1 hour 30 minutes QUESTION AND ANSWER BOOK Section A – Structures and Materials B – Motion • • Structure of book Number of Number of Marks Questions 35 35 9 55 Total 90 Suggested Times (minutes) 45 45 90 Students are permitted to
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Gaunt(67)- extremely thin. 11. Quota(71)- ones share of a total amount. 12. Penchant(75)- a strong liking for something. 13. Embellish (75)- to improve by adding detail. 14. Mundane(76)- unimaginative. 15. remote (81)- far apart. 16. Carnage(81)- massacre. 17. Smug(113)- confident of one’s superiority. 18. Maim(115)- to cripple. 19. undaunted(127)- not forced to abandon purpose or effort. 20. Inflict(134)- to deliver. Chapters 12-19 1. Prohibition (152)- forbidden. 2. Commiserate (158)- pity. 3
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* 2. Choose E such that: 1<E<PQ * E does not have to be prime‚ but must be odd * (P-1)(Q-1) and E must not have no prime factors in common * 3. Compute D such that (DE-1) is evenly divisible by (P-1)(Q-1) * 4. Encryption function is C = (T^E) mod PQ * C is the ciphertext (positive integer) * T is the plaintext (positive integer) * T must be less then the modulus PQ * 5. Decryption function is T = (C^D) mod PQ * C is the ciphertext (positive
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