(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 }
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
360 degree rotation (clockwise or anticlockwise) leaves any figure in exactly the same position as it was at the start. So YOU DO NOTHING.
Answer: 130 degrees. 360x4=1440 degrees. So each time we have 360 degree rotation, we end up where we started. The rotation will be 1575-1440=130 degrees.
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 }
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
change the sign, but DONT switch the coordinates (:
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
we swap the co-ordinates and give the new y co-ordinate the opposite sign.90 degrees clockwise(y, -x)
360 degree rotation (clockwise or anticlockwise) leaves any figure in exactly the same position as it was at the start. So YOU DO NOTHING.
(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.
the numbers
A 90 degree rotation is a quarter of a turn.
The Earth doesn't wobble around its rotation axis. The rotation axis itself rotates,so that the Earth's poles trace around a 23.5-degree circle in the sky, every 26,000years. The term that describes it is "precession".The Earth doesn't wobble around its rotation axis. The rotation axis itself rotates,so that the Earth's poles trace around a 23.5-degree circle in the sky, every 26,000years. The term that describes it is "precession".The Earth doesn't wobble around its rotation axis. The rotation axis itself rotates,so that the Earth's poles trace around a 23.5-degree circle in the sky, every 26,000years. The term that describes it is "precession".
(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.
The Earth doesn't wobble around its rotation axis. The rotation axis itself rotates, so that the Earth's poles trace around a 23.5-degree circle in the sky, every 26,000 years. The term that describes it is "precession".