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Lesson Worksheet: Linear Transformations in Planes: Rotation Mathematics

In this worksheet, we will practice finding the matrix of linear transformation of rotation at a given angle and the image of a vector under a given rotation linear transformation.

Q1:

Describe the geometric effect of the transformation produced by the matrix 22222222.

  • Aa rotation through an angle of 90
  • Ba rotation through an angle of 45
  • Ca rotation through an angle of 45
  • Da rotation through an angle of 90
  • Ea rotation through an angle of 135

Q2:

A rotation with center the origin sends the vector 34 to 43. Find the matrix representation of this rotation.

  • A45353545
  • B24257257252425
  • C45353545
  • D0110
  • E24257257252425

Q3:

A linear transformation of a plane sends the vector 10 to 𝑝𝑞. If the transformation is a rotation about the origin, where does it send 01?

  • A𝑞𝑝
  • B𝑝𝑞
  • C𝑞𝑝
  • D𝑞𝑝
  • E𝑞𝑝

Q4:

A linear transformation of a plane sends vector 10 to 𝑝𝑞. If the transformation is a rotation, where does it send 01?

  • A𝑞𝑝
  • B𝑞𝑝
  • C𝑝𝑞
  • D𝑞𝑝
  • E𝑞𝑝

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