Lesson: Linear Transformations in Planes: Rotation Mathematics

In this lesson, we will learn how to find the matrix of linear transformation of rotation at a given angle and the image of a vector under a given rotation linear transformation.

Lesson Plan

Students will be able to

calculate the image of a single vector under a linear transformation that rotates around the origin,
calculate the image of a shape in the 2D plane under a linear transformation that rotates around the origin,
interpret the geometric effect of applying a given rotation matrix,
find the matrix that represents a rotation by a given angle around the origin,
find the matrix that represents a rotation that sends one point to another point.

Lesson Worksheet

Q1:

Describe the geometric effect of the transformation produced by the matrix .

Q2:

A rotation with center the origin sends the vector to . Find the matrix representation of this rotation.

Q3:

A linear transformation of a plane sends the vector to . If the transformation is a rotation about the origin, where does it send ?