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Q: Does the product of 5 reflections and 8 rotations of the x-y plane produce a rotation or a reflection?

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It will be as you term it 'horizontal stretch' in which the figure is enlarged or reduced in size.

Yes. A rotation by any integer multiple of 45° will produce a figure that will superimpose on the original, un-rotated octagon. 45° 90° 135° 180° 225° 270° 315° as well as a full rotation of 360°.

KJFG, subjected to a rotation, reflection, enlargement, translation or any combination of one or more of these transformations result in a quadrilateral.

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Displacement is defined as moving of something from its position. Rotation is defined as the action of rotating around an axis or center. A geometrical figure can be displaced or rotated in either order to produce the same end result.

Related questions

Reflections, translations, rotations.

A translation, a reflection and a rotation

Translation, rotation, reflection.

Yes, reflection occurs when light bounces off a surface and changes direction. The angle of reflection is equal to the angle of incidence, following the law of reflection. Smooth surfaces tend to produce regular, organized reflections, while rough surfaces scatter light in various directions.

It will be as you term it 'horizontal stretch' in which the figure is enlarged or reduced in size.

Diffused or scattered reflection typically produces a matte or rough surface. This type of reflection occurs when light hits a non-smooth surface and is scattered in multiple directions, creating a soft and uniform appearance without sharp or distinct reflections.

A flat plane mirror produces regular reflections since its polished reflective surface is flat compared to the wavelength of light. If the surface is rough or irregular compared to the wavelength, the light will be scattered, resulting in diffuse reflection.

Yes. A rotation by any integer multiple of 45° will produce a figure that will superimpose on the original, un-rotated octagon. 45° 90° 135° 180° 225° 270° 315° as well as a full rotation of 360°.

Specular refers to a type of reflection in which light is reflected off a smooth surface at a consistent angle, such as with a mirror. It is different from diffuse reflection, where light scatters in various directions off a rough surface. Specular reflections are typically more focused and highlight the shape and details of an object.

A flat mirror produces the most accurate reflection because it preserves the size and shape of the object being reflected without distorting it. Curved mirrors, such as concave or convex mirrors, can produce magnified or distorted reflections.

The kaleidoscope uses the principle of multiple reflections to create symmetrical and colorful patterns. When light enters the kaleidoscope, it bounces off multiple mirrors, creating a series of reflections that produce intricate and changing designs.

If traveling at 30,000,000 mph over a radius of 151.045/2 = 75,522.5 miles the rotational velocity is 30000000/75522.5 = 397.23 radians per hour. Since a rotation is 2 pi radians, that is 63.22 revolutions per hour, or 0.0176 rotations per second