Figures 1 and 2 are two versions of the same system that consists of a pendulum, which defines a reference frame B and rotates relative to a ceiling frame A. In all the systems, r,y, z form a dextral set of orthonormal vectors fixed in reference frame A, and b, by, bz is a dextral set of orthonormal vectors fixed in reference frame B. However, these unit vectors are oriented differently in each system. Compute the direction cosines to fill in each table, and simplify to only refer to sines and cosines (no 90 deg angles floating around). The resulting table is the transformation matrix ARB for each of the systems. (A b B) ARB A b. X Figure 1: Transformation Table, Problem 1(a) A b y A b. 7