Rotation of axes in two dimensions

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Discusses the kinetic energy of solids and the selection of benchmarks and points of affluence.

Covers the calculation of volumes of solids using integrals and provides examples of finding volumes using different functions.

Delves into the historical and geometric aspects of arc concatenation, including ellipse approximation and architectural applications.

Covers the representation and operations in coordinate space with points and vectors.

Explores the construction and variants of elliptical curves, including historical stonecutting methods and architectural considerations.

Covers the definitions of coordinate changes and the Laplacian of a function.

Covers level curves and graphs of functions in two and three dimensions.

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Explores the historical development of celestial geometry and its impact on climate variations and astronomical observations.

Explores coordinate changes between polar and Cartesian coordinates, and introduces the spherical coordinate system.

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