(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
270 rule represent a 270 rotation to the left which is very easy
It is multiplication by the 2x2 matrix 0 1-1 0
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(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
270 rule represent a 270 rotation to the left which is very easy
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
plz awnser this
To rotate a figure 180 degrees clockwise, you can achieve this by first reflecting the figure over the y-axis and then reflecting it over the x-axis. This double reflection effectively rotates the figure 180 degrees clockwise around the origin.
First of all, if the rotation is 180 degrees then there is no difference clockwise and anti-clockwise so the inclusion of clockwise in the question is redundant. In terms of the coordinate plane, the signs of all coordinates are switched: from + to - and from - to +. So (2, 3) becomes (-2, -3), (-2, 3) becomes (2, -3), (2, -3) becomes (-2, 3) and (-2, -3) becomes (2, 3).
It is multiplication by the 2x2 matrix 0 1-1 0
Almost all of the material that formed the Solar system revolved around the Sun in one direction. This represents the conservation of angular momentum when the material contracted to form the Sun and its planetary disk. Since then, collisions and localized gravity have created exceptions to the general counter-clockwise rule (Venus spins slowly clockwise on its axis). The Earth rotates (spins) on its axis counter-clockwise, and orbits the Sun counter-clockwise as well, as viewed from the North Pole of the Earth or Sun. These are arbitrary concepts of "above" and "below" the plane of the Solar System. The Moon also revolves around the Earth counter-clockwise.
The Earth spins counterclockwise (from west to east) because of its initial rotation as a result of the conservation of angular momentum from the cloud of gas and dust that formed the solar system. This spin direction has been maintained due to the lack of significant external influences to change it over time.
The configuration is due to the threading on the screws, which follows a right-hand thread design. When screws are turned clockwise (right), the threads coincide with the direction of rotation, causing them to tighten. Turning screws counter-clockwise (left) engages the threads in a way that causes them to loosen.