(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
The effect of the rotation is the same as that of a 90 degree clockwise rotation. In matrix notation, it is equivalent to [post-]multiplication by the 2x2 matrix: { 0 1 } {-1 0 }
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
It is multiplication by the 2x2 matrix 0 1-1 0
rosting method rule method set-builder rotation
(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
The effect of the rotation is the same as that of a 90 degree clockwise rotation. In matrix notation, it is equivalent to [post-]multiplication by the 2x2 matrix: { 0 1 } {-1 0 }
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.
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
It is multiplication by the 2x2 matrix 0 1-1 0
(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.
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).
(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.
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The direction of rotation of a magnetic field can be determined using the right-hand rule. Point your right thumb in the direction of current flow or field force, and curl your fingers. The direction towards which your fingers curl represents the direction of rotation of the magnetic field.
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