Shown in Figure 1, a coordinate frame rotates along an axis w by an angle 0. Let the frame axis before and after the rotation be x, y, z and x', y', z', respectively. Now, the 3 rotation matrix from the original frame to the new frame is R = 3 4 4 3 2 NIWININ 2 0 1+|+ 1 (a) Obtain the coordinates of each new frame axis x', y', z' in the original frame; (b) Calculate the rotation axis w and angle 0; (c) Let [1 1 1] be the coordinates of a vector w in the original frame, obtain the coordinates of the vector in the new frame. (d) Let Ra = 3 4 3 4 LIN - 1|2 2 NWAWAIH be the attitude of the target frame with respect to the 0 2 original frame x, y, z, what additional rotation is needed with respect to the new frame x', y', z' to achieve this target frame? Figure Z W 0 V X W V 0 1. The coordinate frame before and after rotation.