Mathematics
Grade9
Easy
Question
What is the rotation matrix for 270° rotation?
Hint:
We have the formula for rotation below
![Error converting from MathML to accessible text.](data:image/png;base64,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)
The correct answer is: ![open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets](data:image/png;base64,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)
Rotation matrix for 270° rotation:
![open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets](data:image/png;base64,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)
A rotation matrix can be defined as a transformation matrix that operates on a vector and produces a rotated vector such that the coordinate axes always remain fixed.