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In this lesson, we will learn how to find the matrix of a linear transformation which rotates every vector in R² by a given angle.

Q1:

Consider the linear transformation πΏ β² βΆ β β β 3 3 , which rotates each vector 45 degrees counterclockwise about the positive π₯ -axis then 90 degrees counterclockwise about the positive π¦ -axis. Find in the standard basis.

Q2:

Find the matrix for the linear transformation which rotates every vector in through an angle of .

Q3:

Find the matrix for the linear transformation which rotates every vector in β 2 through an angle of 5 π 1 2 .

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