Just multiply the vector by a rotation matrix:

| fx |     | cos a    -sin a | | sx |
| fy |  =  | sin a     cos a | | sy |

where fx and fy are final coordinates of the object after the rotation and sx, sy are starting one. Obviously a is the angle involved.

Edit: Rotation matrix was incorrect.

Just multiply the vector by a rotation matrix:

| fx |     | cos a    -sin a | | sx |
| fy |  =  | sin a     cos a | | sy |

where fx and fy are final coordinates of the object after the rotation and sx, sy are starting one. Obviously a is the angle involved.

Just multiply the vector by a rotation matrix:

| fx |     | cos a    -sin a | | sx |
| fy |  =  | sin a    -cos a | | sy |

where fx and fy are final coordinates of the object after the rotation and sx, sy are starting one. Obviously a is the angle involved.

Just multiply the vector by a rotation matrix:

| fx |     | cos a    -sin a | | sx |
| fy |  =  | sin a     cos a | | sy |

where fx and fy are final coordinates of the object after the rotation and sx, sy are starting one. Obviously a is the angle involved.

Edit: Rotation matrix was incorrect.