Show that the group of rotations in R3 of a 3-prism (that is, a prismwith equilateral ends, as in the following figure) is isomorphic to D3.

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Q: Let Rn be the group of rotations of a regular pentagon, and let r be counterclockwise rotation by…

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Q: (c) Show that the Euclidean group E(2) is generated by the reflec- tions. More precisely, show that…

A: The Euclidean group E2 is generated by the reflections. That is any isometry of ℝ2 is a product of…

Q: Consider the igure Which transformation would carry trapezoid ABCD onto isei?

A: Trapezoid ABCD given in the graphwe have to find the transformation would carry trapezoid ABCD onto…

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Q: The inverse of the element 5 in the group{1,3,5,7}  is  A)7 B)1 C)5 D)3

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Q: (3) Draw a shape such that the following figure would represent of that shape.

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Q: Preimage: type your answer. Image: type your answer.

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.