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Upgrading from:

Geometry`Rotations`

All the functionality in Geometry`Rotations` is now available in the built-in Mathematica kernel function RotationTransform.

Here is the matrix for rotation by θ degrees:

Version 5.2 << Geometry`Rotations`; MatrixForm[RotationMatrix2D[\[Theta]]]

In Version 6, you get a TransformationFunction that represents a rotation in 2D by θ radians about the origin:

Wolfram Language code: r = RotationTransform[-θ]

The point {0,0} is rotated about the point {1,1} by 60 degrees:

Version 5.2 << Geometry`Rotations`; MatrixForm[RotationMatrix2D[N[Pi/3]]]; Rotate2D[{0., 0.}, N[Pi/3], {1., 1.}]
Wolfram Language code: r = RotationTransform[N[-Pi / 3], {1, 1}]
Wolfram Language code: r[{0., 0.}]

RotationMatrix rotates points in the opposite direction from RotationMatrix2D:

Version 5.2 << Geometry`Rotations`; RotationMatrix2D[phi]
Wolfram Language code: RotationMatrix[-phi]

Similarly RotationTransform rotates points in the opposite direction from Rotate2D:

Version 5.2 << Geometry`Rotations`; Rotate2D[{x, y}, phi, {x0, y0}]
Wolfram Language code: RotationTransform[-phi, {x0, y0}][{x, y}]

RotationMatrix uses yaw-pitch-roll angles rather than the Euler angles used by RotationMatrix3D:

Version 5.2 << Geometry`Rotations`; RotationMatrix3D[phi, theta, psi]
Wolfram Language code: RotationMatrix[Pi - psi, {0, 0, 1}].RotationMatrix[theta, {1, 0, 0}].RotationMatrix[Pi - phi, {0, 0, 1}]