1. (a) Let A be the set of all 2 × 2 matrices of the form ‚ where a and b are 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
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Exploration of Lacsap’s Fractions The following will be an investigation of Lacsap’s Fractions‚ that is‚ a set of numbers that are presented in a symmetrical pattern. It is an interesting point that ‘Lacsap’ is ‘Pascal’ backwards‚ which hints that the triangle below will be similar to “Pascal’s Triangle”. 1 1 1 1 1 1 1 1 1 1 There are many patterns evident in this triangle‚ for instance I can see
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grow over the years‚ it is certain that we should also acknowledge that other countries will be expanding also. We tend to focus how each country is growing in technology but there are many other trends that we are forgetting. Youths in China and India tend to follow their own trends. We will discuss China and India by describing the products (goods and services) that interest their youth markets‚ comparing and contrasting the micro- and macro-environmental forces that can influence the marketing strategies
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I. INTRODUCTION II. TREND IN POPULATION AGING IN CHINA III. INCREASE RATE OF TOTAL AND ELDERLY POPULATION IV. IMPACT OF THE RISING ELDERLY ON ECONOMIC SOCIAL SYSTEMS V. ECONOMIC EFFECTS ON CHINA’S ECONOMY VI. CURRENT SOCIAL PROGRAMS FOR THE ELDERLY VII. FUTURE SOCIAL PROGRAMS FOR THE ELDERLY VIII. POSSIBLE ECONOMIC IMPACT ON LABOR‚ FAMILY‚ AND WORKING-AGE
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1.5 billion population in china‚ thus there is huge vehicle market in china. Though 26 years development of vehicle market which is going to saturation. The vehicle producers have to find new vehicle market space in china. With an increasing demand in the vehicle market in China‚ and the trend for Chinese females to become more independent‚ it is crucial to find out whether there is a trend in the female market in China and how to attract female consumers to the car market in China. To achieve the
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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M07/5/MATHL/HP1/ENG/TZ1/XX/M MARKSCHEME May 2007 MATHEMATICS Higher Level Paper 1 16 pages -2- M07/5/MATHL/HP1/ENG/TZ1/XX/M This markscheme is confidential and for the exclusive use of examiners in this examination session. It is the property of the International Baccalaureate and must not be reproduced or distributed to any other person without the authorization of IBCA. -3- M07/5/MATHL/HP1/ENG/TZ1/XX/M
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China’s One Child Policy Population policies are the measures taken by the government to influence the population growth of the country. There are two types of population policies‚ which are pro-natalist and anti-natalist. A pro-natalist policy is a policy where the main objective is to increase birth rates and total fertility rate. However‚ a person cannot be forced to have children. As a result‚ the government tries to offer incentives to such as free education‚ and extended maternity leave
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IB Math SL Type II Internal Assessment High Jump Heights Aim: The aim of this task is to consider the winning height for the men’s high jump in the Olympic Games. The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games. Year | 1932 | 1936 | 1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 1980 | Height(cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 | Note: The Olympic Games were not held in 1940 and
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SL TYPE 1-LACSAP’S FRACTIONS * INTRODUCTION This investigation is going to do research patterns relates to the Lacsap’s Fractions. For its external structure‚ Lacsap’s Fraction is analogous to Pascal’s Triangle. Lacsap’s Fraction presents the way of generating and organizing the binomial coefficients. Within this investigation‚ the work is planning to be divided into two parts. In the first part‚ the content will relate to the pattern of numerators. In the second part‚ I am going to do the
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M11/5/MATME/SP1/ENG/TZ1/XX 22117303 mathematics staNDaRD level PaPeR 1 Wednesday 4 May 2011 (afternoon) 1 hour 30 minutes iNSTrucTioNS To cANdidATES candidate session number 0 0 Examination code 2 2 1 1 – 7 3 0 3 Write your session number in the boxes above. not open this examination paper until instructed to do so. do are not permitted access to any calculator for this paper. You Section A: answer all questions in the boxes provided. Section B: answer all questions on the
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