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Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations , which have no fixed points, and (hyperplane) reflections , each of them having an entire ( n − 1) -dimensional flat of ...
In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly. [2] [3] A rotation of axes is a linear map [4] [5] and a rigid transformation.
Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other (see figures). On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The area element is given in (X, Y) coordinates by
Google Maps, which relied on it since 2005, still uses it for local-area maps but dropped the projection from desktop platforms in 2017 for maps that are zoomed out of local areas. Many other online mapping services still exclusively use the Web Mercator.
At point P 21 the circle intersects with the unity circle of constant normalised resistance at z P 21 = 1.00 + j 1.52 {\displaystyle z_{P21}=1.00+j1.52\,} . The extension of the line OP 21 intersects the wavelength scale at L 2 = 0.177 λ {\displaystyle L_{2}=0.177\lambda \,} , therefore the distance from the termination to this point on the ...
With an area of 37 million square kilometres, it makes up approximately 10% of the Earth's ocean surface. [3] The gyre , as with Earth's other four gyres, contains an area with elevated concentrations of pelagic plastics, chemical sludge , and other debris known as the South Pacific garbage patch .
Google Maps Street View Trekker backpack being implemented on the sidewalk of the Hudson River Greenway in New York City. In late 2014, Google launched Google Underwater Street View, including 2,300 kilometres (1,400 mi) of the Australian Great Barrier Reef in 3D. The images are taken by special cameras which turn 360 degrees and take shots ...
For instance, consider reflection in a vertical line and a line inclined at 45° to the horizontal. One can observe that one composition yields a counter-clockwise quarter-turn (90°) while the reverse composition yields a clockwise quarter-turn. Such results show that transformation geometry includes non-commutative processes.