5 - Rotation tensor
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Practice Questions
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Define a rotation tensor in your own words.
💡 Hint: Think about the physical meaning of rotating an object.
What is the determinant of a rotation matrix?
💡 Hint: Consider how volume changes during rotation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a fundamental property of rotation tensors?
💡 Hint: Consider what happens when you spin an object.
True or False: The determinant of a rotation matrix is less than one.
💡 Hint: Reflect on the conservation of volume during rotations.
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Challenge Problems
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If a vector (2, 0, 0) is rotated 90 degrees around the z-axis, what will be its new coordinates?
💡 Hint: Use the rotation matrix: R = [[0, -1, 0], [1, 0, 0], [0, 0, 1]].
Consider a 3D object being rotated in a simulation. How can rotation tensors ensure that its size remains consistent?
💡 Hint: Reflect on the properties of orthonormal matrices.
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