<s>[INST] I want to implement a rotation in 2d: given an angle for x and y rotation how are the corresponding matrices for rotation around the x and y axis computed? [/INST] For rotating a 2D point around the x-axis by an angle "theta", the matrix is:

1, 0, 0
0, cos(theta), -sin(theta)
0, sin(theta), cos(theta)

For rotating a 2D point around the y-axis by an angle "theta", the matrix is:

cos(theta), 0, sin(theta)
0, 1, 0
-sin(theta), 0, cos(theta)

In these matrices, "theta" is the angle of rotation, "cos(theta)" is the cosine of the angle, and "sin(theta)" is the sine of the angle. The angles are usually given in radians.</s>\ <s>[INST] Given two 3x3 state matrices, find the 3 angles Ω,Π,μ that makes the rotation from the first to the second, do an example with random numbers [/INST] 