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- TransformedRegion[Ellipsoid[{x, y}, {r1, r2}], RotationTransform[Θ, {x, y}]]
- Ellipsoid[{x, y},
- {{r1^2 Cos[Θ]^2 + r2^2 Sin[Θ]^2, r1^2 Cos[Θ] Sin[Θ] - r2^2 Cos[Θ] Sin[Θ]},
- {r1^2 Cos[Θ] Sin[Θ]] - r2^2 Cos[Θ] Sin[Θ], r2^2 Cos[Θ]^2 + r1^2 Sin[Θ]^2}}]
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