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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• Type 1 Type 1 often affects people under 30 years of age but can develop at any time. In Type 1 diabetes‚ your pancreas stops making insulin or only makes a very small amount. Without insulin‚ glucose cannot enter into your cells which need to burn glucose for energy. Some people are born with the genes‚ but only some will develop it. While there is no such thing as a good or bad diabetic‚ some individuals have very wide‚ unsteady swings in blood sugars. This happens when their bodies have extreme
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Complex Numbers and Applications ME50 ADVANCED ENGINEERING MATHEMATICS 1 Complex Numbers √ A complex number is an ordered pair (x‚ y) of real numbers x and y. For example‚ (−2.1‚ 3.5)‚ (π‚ 2)‚ (0‚ 0) are complex numbers. Let z = (x‚ y) be a complex number. The real part of z‚ denoted by Re z‚ is the real number x. The imaginary part of z‚ denoted by Im z‚ is the real number y. Re z = x Im z = y Two complex numbers z1 = (a1‚ b1) and z2 = (a2‚ b2) are equal‚ written z1 = z2 or (a1‚ b1) = (a2‚ b2)
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Organization 2012 Mathematical studies SL: Formula booklet 1 5045 Contents Prior learning Topics Topic 1—Algebra Topic 2—Functions and equations Topic 3—Circular functions and trigonometry Topic 4—Vectors Topic 5—Statistics and probability Topic 6—Calculus 2 3 3 4 4 5 5 6 Mathematics SL formula booklet 1 Formulae Prior learning Area of a parallelogram Area of a triangle A= b × h = A 1 (b × h) 2 1 ( a + b) h 2 Area of a trapezium = A Area of a circle
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In dramatic construction there must be variation of pace and rhythm‚ monotony of any kind being certain to induce boredom. Comparing at least two plays you have studied in the light of this statement‚ show how variations of pace and rhythm have been used to attract of heighten the interest of the audience. Within Tennessee Williams A Streetcar Named Desire and Arthur Miller s The Crucible variations of pace and rhythm are utilized in order to attract or heighten the attention of the audience. However
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numerator added by one plus the row number. Using this general statement it can be concluded that the numerator in the 6th row is 21 (15+6)‚ and 28 for the 7th. Generating a Statement for the Numerator: To generate an equation for the numerator of the fraction‚ the fraction data must be organized and graphed. The table below shows the relationship between the row number and numerator being relative to an exponential function as the sequence goes on. N(n+1)-Nn represents the equation for the
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Chapter 1 Number and Set FHMM1014 Mathematics I 1 Content 1.1 Real Numbers System. 1.2 Indices and Logarithm 1.3 Complex Numbers 1.4 Set FHMM1014 Mathematics I 2 1.1 Real Numbers FHMM1014 Mathematics I 3 Real Numbers • Let’s review the types of numbers that make up the real number system. FHMM1014 Mathematics I 4 Real Numbers i). Natural numbers (also called positive integers). N = {1‚ 2‚ 3‚…..} ii). Integers. Natural numbers‚ their negatives and zero. Z = {…….‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3
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Predictability of Social Media Usage to Grade Averages IB Math Studies Spring 2013 Table of Contents: Introduction/Purpose……………………………………………………………..p.3 Data Collection Method……………………………………………………….....p. 3 - 4 Data Analysis: Chi-Squared Statistic Frequency Table…………………………………………………………p. 4 - 5 Contingency Table……………………………………………………….p. 5 – 6 Chi – Squared Statistic…………………………………………………...p. 7 Degrees of Freedom………………………………………………………p. 7 Critical Value……………………………………………………………
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c IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M05/1/A1ENG/HP1/ENG/TZ0/XX/M MARKING NOTES REMARQUES POUR LA NOTATION NOTAS PARA LA CORRECCIÓN May / mai / mayo 2005 ENGLISH / ANGLAIS / INGLÉS A1 Higher Level Niveau Supérieur Nivel Superior Paper / Épreuve / Prueba 1 5 pages/páginas -2- M05/1/A1ENG/HP1/ENG/TZ0/XX/M These marking notes are confidential and for the exclusive use of examiners in this examination session. They are the property of the International
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simple curve on the ground using the method of deflection when the entire curve is visible from the beginning of curve (B.C.). II. Instruments 1 unit - Engineers transit 1 pc - Plumb bob 1 roll - string 1 pc - 50-meter tape 10 pcs - marking pins Procedure A. Data and Computations 1. The following data (obtained from a preliminary survey) and assumed standards will be used to layout the desired curve-centerline in the field.
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