A rotation matrix R is a 3 times 3 matrix which describes the relative orientation of two objects, for example the orientation of the nose and wings of an aircraft relative to the surface of the Earth. Three angles, the Euler angles, are required to describe an arbitrary orientation and its corresponding matrix: the roll angle o, the pitch angle theta. and the yaw angle With these three angles, ft can be computed using R (phi, theta, psi) = R_2(0) R_y(theta) R_z(phi) where R_x(psi) = [1 0 0 0 cos psi -sin psi 0 sin psi cos psi], R_y (theta) = [cos theta 0 sin theta 0 1 0 -sin theta 0 cos theta], R_2 = [cos psi -sin psi 0 sin psi cos psi 0 0 0 1] This formula for the rotation matrix R uses the product of three matrices. Matlab's * operator works correctly between matrices to carry out such multiplications. Be careful, however, because matrix multiplication is not commutative, so the multiplications must be carried out in the exact order shown to correctly compute R. Write a Matlab script called rot. A which will construct the rotation matrix R for any specified sot of Euler angles. Your script should assume that the angles phi. theta. and psi have been defined iu the workspace, and use the variable R to hold the final result. It is not necessary for your script to actually show the values stored in R. If you have written your function correctly, you should be able to reproduce this result >> clear; phi=0; theta=pi/2; psi=pi; >> rot >> w - R* [1;-2;3] v = -3 2 -1 In the last line, the rotation matrix R is multiplying a three dimensional vector. As you shall see in your junior level dynamics classes, such multiplications serve to convert vectors expressed in one coordinate frame (for example, a frame embedded in the aircraft) to a different frame (for example, one fixed to the surface of the Earth)