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  1. Rotation: This is defined as movement of a point P(x,y) in a plane by an angle θ to another position...clockwise direction, then the equivalent angle in counter clockwise direction is given by (360-θ). In these rotation in counter clockwise direction, the new position of Q(x₁,y₁), is given by: (x₁...

    1 Answers · Science & Mathematics · 26/05/2011

  2.   We need to rotate θ degrees. Rotation matrix: [X] = [ cosθ −sinθ ] [ x ] [Y]  [ sinθ  cosθ ] [ y ] [x...

    2 Answers · Science & Mathematics · 01/12/2016

  3. After the second rotation, it would be at (imagine just rotating (sqrt(2)/2, 0, 0) first) at... a bit more difficult to see, but follows but simply doing the rotation to the last two coordinates. Another thing to be careful of: the...

    1 Answers · Science & Mathematics · 30/08/2008

  4. ...the purpose of considering the effects of rotations and reflections, it might be worthwhile to think...the point (x, y) becomes the point (y, -x) after rotation. Reflection across a vertical line -- ...

    1 Answers · Science & Mathematics · 31/10/2016

  5. If A is the rotation angle of the new co-ordinate system, we can express the current x, y co-ordinates...

    1 Answers · Science & Mathematics · 07/04/2014

  6. ...there are many different ways to represent rotations mathematically. First, complex numbers can...for you to work out. Now, keep in mind that rotations can also be represented by matrices...

    2 Answers · Science & Mathematics · 12/07/2008

  7. ...and y' in the opposite direction to get x and y. Let t be the the angle of rotation. So the substitution we will be using is x = x' cos t - y...

    2 Answers · Science & Mathematics · 01/06/2013

  8. A rotation by 90° about the origin. The general rule for a rotation by 90° about the origin...the object. lets say you have a point P(2,-3). The 90 degree rotation would place it at P'(3,2) under our general rule. You will see...

    1 Answers · Science & Mathematics · 14/05/2010

  9. Rotation and translation are "affine" transformations. So if you have a set of points... will be the same as the corresponding two points in Y. So, in summary, rotations and translations are affine transformations and therefore: 1) Angles are...

    2 Answers · Science & Mathematics · 14/12/2008

  10. Since you give only one angle for each rotation, I assume you mean they are rotations... counterclockwise (θ=180º) (180º rotation is the same in either direction): (x,y) → (-x, -y) ...

    2 Answers · Science & Mathematics · 09/11/2012

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