Introduction to Matlab: Application to Electrical Engineering Houssem Rafik El Hana Bouchekara Umm El Qura University (version 1‚ Februray 2011) 1 Contents 1 CHAPTER 1 ............................................................................................................................................ 7 1.1 TUTORIAL LESSONS 1 ................................................................................................................................ 7 1.1.1 1.2 STARTING AND QUITTING
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Physics Content with Answers 1. In the absence of air resistance‚ a ball of mass m is tossed upward to reach a height of 20 m. At the 10m position‚ half way up‚ the net force on the ball is A. 2mg. B. mg. C. mg/2. D. mg/4. B is correct‚ as a vector diagram would show. Other choices show carelessness or confusion between force and speed‚ and what constant acceleration means. 2. When you drop a ball it accelerates downward at 9.8 m/s2. If you instead throw it downward‚ then its acceleration
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<> Usually when testing for XSS vulnerabilities‚ we normally use the attack vectors <script>alert(111)</script> ‚ <body onload=alert(111)/> etc. If the developer has implemented a blacklist serverside validation for <> and script‚ we will not get satisfactory test results. But in some scenarios we can successfully demonstrate an XSS attack even without using the above mentioned vectors. This new scenario is mainly observed in the “Search” text box of the applications
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into the subtopics of kinematics and dynamics. Kinematics is concerned with the aspects of motion that exclude the forces that cause motion. In a manner of speaking‚ kinematics is focussed on the development of definitions: position‚ displacement‚ velocity‚ acceleration and on the relationships that exist between them. Dynamics widens the study of motion to include the concepts of force and energy. Definitions Position Kinematics begins with the idea of position. Suppose that we photograph an object
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of a matrix (with real or complex entries‚ say) is zero if and only if the column vectors of the matrix are linearly dependent. Thus‚ determinants can be used to characterize linearly dependent vectors. For example‚ given two linearly independent vectors v1‚ v2 in R3‚ a third vector v3 lies in the plane spanned by the former two vectors exactly if the determinant of the 3 × 3 matrix consisting of the three vectors is zero. The same idea is also used in the theory of differential equations: given n functions f1(x)
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. . . . . . 1.3.1 Orthogonal Vectors . . . . . . . . . . . . . . . . . . 1.3.2 Orthogonal Space . . . . . . . . . . . . . . . . . . . 1.3.3 Gram-Schmidt Orthogonalization Process . . . . . 1.4 Orthogonal Projectors . . . . . . . . . . . . . . . . . . . . 1.4.1 Linear Projectors . . . . . . . . . . . . . . . . . . . 1.4.2 Orthogonal Projections . . . . . . . . . . . . . . . . 1.4.3 Symmetric Endomorphisms and Matrices . . . . . 1.4.4 Gram Matrix of a Family of Vectors . . . . . . . . . 1.4.5 Orthogonal
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S CHNEIDER J.‚ KONDRATIEVA P.‚ K RÜGER J.‚ W ESTERMANN R.: Interactive visual exploration of unsteady 3D-flows. In Eurographics/IEEE VGTC Symposium on Visualization (2007)‚ pp. 251–258. [GKP07] G RIFFITH E. J.‚ KOUTEK M.‚ P OST F. H.: Fast normal vector compression with bounded error. In Proc. Geometry Processing. (2007)‚ pp. 263–272. [GPK∗ 05] G RIFFITH E. J.‚ P OST F. H.‚ KOUTEK M.‚ H EUS T.‚ J ONKER H. J. J.: Feature tracking in VR for cumulus cloud life-cycle studies. In Virtual Environments
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Section 2.2 Matrices in Matlab 75 2.2 Matrices in Matlab You can think of a matrix as being made up of 1 or more row vectors of equal length. Equivalently‚ you can think of a matrix of being made up of 1 or more column vectors of equal length. Consider‚ for example‚ the matrix 1 2 3 0 A = 5 −1 0 0 . 3 −2 5 0 One could say that the matrix A is made up of 3 rows of length 4. Equivalently‚ one could say that matrix A is made up of 4 columns of length 3. In either model‚ we have 3 rows
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ENERGY SYSTEMS Figure 1 shows a sprint cycle race. This activity involves cycling four laps of a 250 metre track‚ with the final lap being completed as fast as possible. Elite performers cover the final lap in times of between 10 and 11 seconds. (a) Name the main energy system being used in the final sprint to the finishing line and explain how this system provides energy for the working muscles. (4 marks) (b) At the end of the race‚ the cyclist will be out of breath and will continue to breathe
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Rectangular Coordinates Cylindrical Coordinates Spherical Coordinates Line Integrals of Vectors The component of a vector along a given path is found using the dot product. The resulting scalar function is integrated along the path to obtain the desired result. The line integral of the vector A along a the path L is then defined as shown in fig. Where dl = al dl al : unit vector in the direction of the path L dl : differential element of length along the path L A
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