Final answer:
To find the angle of rotation for each matrix, use the general rotation matrix and the unit circle. Use inverse trigonometric functions or find the reference angle on the unit circle.
Step-by-step explanation:
To find the angles of rotation for the given matrices, we can use the general rotation matrix and the unit circle. The general rotation matrix for a rotation angle of θ is:
[cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
The unit circle is a circle with a radius of 1 unit.
The angles of rotation can be found by using inverse trigonometric functions or by finding the reference angle on the unit circle.
For example, to find the angle of rotation for 30°, we can use sin(30°) = 0.5 to find the reference angle of 30° on the unit circle. Similarly, for 60°, sin(60°) = √3/2, and for 150°, sin(150°) = -0.5.