Describe a deformation of the (x, y) plane. Find the matrix C which diagonalizes M and the matrix D which gives the deformation relative to the new axes.
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- Vector u = <-7,3,-5> and vector v = <-1,1,0>. Find the cross product of 9(u X v)Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is P = 35 kN in member A and Q=10 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B. 40° A -20° The magnitude of the resultant of the forces applied to the bracket by members A and B is The direction of the resultant of the forces applied to the bracket by members A and B is KN.The strain components εx, εy, and γxy are given for a point in a body subjected to plane strain. Determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle θp, the principal strain deformations, and the maximum in-plane shear strain distortion on a sketch. εx = -750 με, εy = -345 με, and γxy = 1250 μrad. Enter the angle such that -45°≤θp≤ +45°.
- Using spherical polar coordinates r, 0, p to find CM of a uniform solid hemisphere of radius R, whose flat face lies in the xy plane with its center at the origin. The element of volume is in spherical polars of dV = r² dr sine de dip.Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following steps. For each step, the distance (in meters) and direction in which you move A. are given by the cross product A x B of the given vectors A and B. For example, the first move is 18 m in the +z direction. What is the magnitude dnet of your final displacement from the origin? (a) A = 3.01, B = 6.0 (b) A = - 4.01, B = 3.0k - (c) A = 2.0₁, B = 4.0k (d) A = 3.0₁, B - 8.0 (e) A = 4.0K, B = - 2.01 (f) A = 2.01, B - 4.01The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled A→ through D→. This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. What is the x component of A→?