# Video: Finding the Matrix of Linear Transformation of Rotating Vectors in Two Dimensions through a Given Angle

Find the matrix for the linear transformation that rotates every vector in βΒ² through an angle of π/3.

01:20

### Video Transcript

Find the matrix for the linear transformation that rotates every vector in β squared through an angle of π over three.

This kind of rotation takes each vector and moves them to a new position by rotating them about a certain angle. We can use a rotation matrix here. We can rotate the vectors β by π using this matrix, cos π, sin π, negative sin π, cos π.

If we want to rotate about π over three, weβre making a 60-degree rotation. We would take cos of π over three, sin of π over three, negative sin of π over three, and then cos of π over three again. We know cos of 60 degrees equals one-half. And sin of 60 degrees equals the square root of three over two. Using that information, we plug in what we know.

And weβll have one-half, square root of three over two, negative square root of three over two, and one-half. This is the matrix we would need to rotate every vector by an angle of π over three.