1. Calculate the rotation matrix for an aircraft with yaw ?=45, pitch ?=15, and roll ?=5.
2. Consider an alternate 1-2-3 set of Euler angles: rotation about the 1-axis through angle ?1, then rotation about the 2-axis through angle ?2, and finally rotation about the 3-axis through angle ?3. Calculate the rotation matrix for angles ?1=5, ?2=15, and ?3=45. Does this represent the same orientation as the aircraft in Problem 1?
Please provide clear and easy to follow steps.