An angle between vectors p and r has a measure of 120°.lf |p| =8 and |r|=8, calculate p(p-r).

Let A be an orthogonal n times n matrix. (1) Prove that for every vectors x vector, y vector elementof R^n, the angle between A x vector and A y vector is the same as the angle between x vector and y vector (in this case, we say that A keeps the angle). (2) Find a matrix B, such that B keeps the angle in the sense of part (a) but B is not orthogonal.

The characteristic equation of the matrix A = [5 4 1 -3] is a. lambda^2 - 2 lambda - 19 = 0 b. lambda^2 + 2 lambda - 19 = 0 c. lambda^2 - 2 lambda + 19 = 0 d. lambda^2 + 2 lambda + 19 = 0 Cosine value of the angle between vectors u and v is 1 and ||u|| = 3, ||v|| = 5, then (u, v) a. 10 b. 15 c. Squareroot 15 d. Squareroot 10