Let v=5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector point?
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16. Let T:R2 R2 be a non-zero linear transformation with standard matrix A, and let det(A) = 0. Which of the following statements is true? A) The parallelogram formed by T . and T0 ) has area 1. B) There is a linear transformation S: R2 + R2 such that SoT is the identity transformation. C) dim (span {7 ( 6 ) 7( ')}) – 1. D) For every vector b E R2, there is a vector u € R2 such that T(u) = b.
This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body rotating about the z-axis. The rotation can be described by the vector where is the angular speed of B, that is, the tangential speed of any point P in B divided by the distance d from the axis of rotation.
Let be the position vector of P.
(a) By considering the angle in the figure, show that the velocity field of b is given by .
(b) Show that
(c) Show that curl
1. SHOW ALL YOUR WORK! (10 MARKS] Let OAB be a triangle with vertices 0(0,0), A(10,0), B(6, 12). Find the dimensions of the rectangle with maximum area inscribed in the triangle and with one of its sides on the side O A of the triangle.
