(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.
Three quarters of a turn clockwise is equivalent to a 270-degree rotation in that direction. Starting from a position facing forward, this rotation would turn you to face directly downward. Essentially, it moves you three-quarters of the way around a circle.
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.
To perform a 180-degree clockwise rotation of a point ((x, y)) around the origin in a Cartesian coordinate system, the formula is given by ((x', y') = (-x, -y)). This effectively inverts both the x and y coordinates, resulting in a point located directly opposite on the Cartesian plane.
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.
To find the image of the point (1, -6) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The coordinates transform as follows: (x, y) becomes (y, -x). Therefore, the image of (1, -6) is (-6, -1).
A 180-degree turn clockwise refers to rotating an object or position halfway around a circle in the clockwise direction. This means that if you start facing a certain direction, after the turn, you will be facing directly opposite that initial position. For example, if you begin facing north, a 180-degree clockwise turn will leave you facing south. This type of rotation is commonly used in various contexts, including navigation and sports.
To find the image of the point (4, 3) after a -90-degree rotation (which is equivalent to a 90-degree clockwise rotation), you can use the rotation formula: (x', y') = (y, -x). Applying this to the point (4, 3), the new coordinates become (3, -4). Therefore, the image of the point (4, 3) after a -90-degree rotation is (3, -4).
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.
The earth's orbit is the path along which the earth travels around the sun. The earth's axis is always inclined to its orbital plane at an angle of 66 and a half degree. shannon is awesome