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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HYDRAULIC JUMP ABSTRACT In this paper‚ the group proposes an analytical representation for the occurrence of hydraulic jump flow. The experiment showed that hydraulic jumps happen when a high velocity liquid enters a zone of lower velocity. The approach used by the group is controlled volume method‚ as it is the most commonly used approach in analyzing hydraulic jumps. Using the Reynolds Transport Theorem and with the aid of some very helpful assumptions‚ the group
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Higher Level Mathematics Internal Assessment Type I Shadow Functions Contents Introduction: Functions/Polynomials 3 Part A: Quadratic Polynomials 4 Part B: Cubic Polynomials 12 Introduction: In mathematics‚ function is defined as a relationship‚ or more of a correspondence between the set of input values and the set of output values. Also‚ a rule is involved‚ or as it may be referred to‚ a ‘set of ordered pairs’ that assigns a unique output for each of the input. The
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Title: Understanding Jump Racing & Flat Racing Description: Having knowledge about the two major types of horse racing types—Jump & Flat Racing—are essential know about for first-time bettors. Keyword: point spread betting Some people may have the impression that all horse races are alike; however‚ horse racing is actually a diverse sporting event. It goes back hundreds of years and has undergone significant changes throughout its history. These days racing occurs in a selection of formats with
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Introduction When we think of bees‚ what do we think of? Do we think about getting stung? The sweet honey that they make? What about their crazy mathematical genius? Bees have‚ somehow‚ figured out that they should use hexagons for their honeycombs. How? I hove no clue- do I look like an apiologist to you? No. But I do know that the method the bees use is the best method for their intent. The unit “Do Bees Build It Best?” helped me realize and confirm the previous. I studied geometry
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& HYDRAULIC JUMP EXPERIMENT MEMBERS | MATRIC NUMBER | 1) MOHAMAD SHAHRUL IZAAN BIN AFANDI | KEA090015 | 2) MOHD KUSHAIRI BIN MOHAMMAD DARUS | KEA090017 | 3) NUR AMALIENA BINTI AHMAD PAKRI | KEA090029 | 4) NUR SOFIAH BTE HARUN | KEA090031 | 5) ROZITA BINTI SARIAN | KEA090033 | INTRODUCTION HYDRAULIC JUMP Hydraulic jump is the natural phenomenon that always occurs at the open channel flow like river and spillway. This phenomenon occurred when a high velocity liquid
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E High-Intensity Resistance Training Improves Glycemic Control in Older Patients With Type 2 Diabetes DAVID W. DUNSTAN‚ PHD1 ROBIN M. DALY‚ PHD2 NEVILLE OWEN‚ PHD3 DAMIEN JOLLEY‚ MSC2 MAXIMILIAN DE COURTEN‚ MD1 JONATHAN SHAW‚ MD1 PAUL ZIMMET‚ PHD1 ommend the use of resistance training as part of a well-rounded exercise program for older individuals. However‚ the role of progressive resistance training as a treatment regimen for improving the metabolic profile of older patients with type 2 diabetes
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Determining the equilibrium constant from pH values of changing concentrations of ethanoic acid Design Research question: How will altering the concentrations of ethanoic acid affect the pH value‚ and‚ in-turn‚ the equilibrium constant? Background information: When weak acids react‚ the reaction typically does not go to completion. Rather‚ the system goes to an intermediate state in which the rates of the forward and reverse reactions are equal. Such a system is said to be in chemical equilibrium
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Laboratory Report for Sluice Gate and Hydraulic Jump Introduction. In this lab exercise we were supposed to analyse the Hydraulic jump through the Sluice gate‚ and to discuss about the energy displacement through that process. Hydraulic jump is known as the change flow which changes from the supercritical flow to the sub-critical flow‚ this change occurs due to the loss turbulence in an open tunnel. In basic terms this happens when there is a sudden rise in the water levels‚ due to the
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Finding the equation of the line which passes through A and B Finding C and D‚ the other points of intersection Ratio of distance between CA‚ AB and BD Notice how if Therefore‚ the function will not have 2 points of inflection‚ thus will not be a Golden Quartic‚ and points A and B‚ the non-stationary points of inflection will be non-existent and hence‚ the distance between the points will also be non-existent‚ as shown below: Investigation #5
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