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In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
X-Y tables, also known as cross working tables or coordinate tables, help provide horizontal motion for automated machinery such as assembly robots in manufacturing facilities. Robotic arms and other automated machinery have only a limited range of motion while their bases remain stationary; X-Y tables allow this basis to move horizontally ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth. Therefore, the horizontal coordinate system is sometimes called the az/el system, [1] the alt/az system, or the alt-azimuth system, among
But the tables must wrap (one dropping below the other) in narrow screens if horizontal scrolling is to be avoided. Narrow your browser window to see the tables below wrap. This works in mobile view too. Click on "mobile view" at the bottom of any Wikipedia page. These tables are adapted excerpts from versions of Iceland men's national handball ...
Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation ).
By rotating the cube by 45° on the x-axis, the point (1, 1, 1) will therefore become (1, 0, √ 2) as depicted in the diagram. The second rotation aims to bring the same point on the positive z-axis and so needs to perform a rotation of value equal to the arctangent of 1 ⁄ √ 2 which is approximately 35.264°.
For a change of basis, the formula of the preceding section applies, with the same change-of-basis matrix on both sides of the formula. That is, if M is the square matrix of an endomorphism of V over an "old" basis, and P is a change-of-basis matrix, then the matrix of the endomorphism on the "new" basis is .