Ad
related to: double rotation of a plane shape activity exampleseducation.com has been visited by 100K+ users in the past month
It’s an amazing resource for teachers & homeschoolers - Teaching Mama
- Lesson Plans
Engage your students with our
detailed lesson plans for K-8.
- Digital Games
Turn study time into an adventure
with fun challenges & characters.
- Interactive Stories
Enchant young learners with
animated, educational stories.
- Printable Workbooks
Download & print 300+ workbooks
written & reviewed by teachers.
- Lesson Plans
Search results
Results from the WOW.Com Content Network
The plane of rotation is the plane orthogonal to this axis, so the axis is a surface normal of the plane. The rotation then rotates this plane through the same angle as it rotates around the axis, that is everything in the plane rotates by the same angle about the origin.
If the rotation angles are unequal (α ≠ β), R is sometimes termed a "double rotation". In that case of a double rotation, A and B are the only pair of invariant planes, and half-lines from the origin in A, B are displaced through α and β respectively, and half-lines from the origin not in A or B are displaced through angles strictly ...
The case of θ = 0, φ ≠ 0 is called a simple rotation, with two unit eigenvalues forming an axis plane, and a two-dimensional rotation orthogonal to the axis plane. Otherwise, there is no axis plane. The case of θ = φ is called an isoclinic rotation, having eigenvalues e ±iθ repeated twice, so every vector is rotated through an angle θ.
Rotation matrices have a determinant of +1, and reflection matrices have a determinant of −1. The set of all orthogonal two-dimensional matrices together with matrix multiplication form the orthogonal group: O(2). The following table gives examples of rotation and reflection matrix :
The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its fixed points. They exist only in n = 3. The plane of rotation is a plane that is invariant under the rotation. Unlike the axis, its points are not fixed themselves.
For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...
Also called an n-fold improper rotation axis, it is abbreviated S n. Examples are present in tetrahedral silicon tetrafluoride, with three S 4 axes, and the staggered conformation of ethane with one S 6 axis. An S 1 axis corresponds to a mirror plane σ and an S 2 axis is an inversion center i.
Reflection. Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2.(F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c.
Ad
related to: double rotation of a plane shape activity exampleseducation.com has been visited by 100K+ users in the past month
It’s an amazing resource for teachers & homeschoolers - Teaching Mama