RotationMatrix

RotationMatrix[θ] gives the 2D rotation matrix that rotates 2D vectors counterclockwise by θ radians.

RotationMatrix[θ, w] gives the 3D rotation matrix for a counterclockwise rotation around the 3D vector w.

RotationMatrix[{u, v}] gives the matrix that rotates the vector u to the direction of the vector v.

Examples

2D rotation matrix:

RotationMatrix[Pi/4]
(* {{1/Sqrt[2], -1/Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}} *)

3D rotation around z-axis:

RotationMatrix[Pi/2, {0, 0, 1}]
(* {{0, -1, 0}, {1, 0, 0}, {0, 0, 1}} *)

Please visit the official Wolfram Language Reference for more details.