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A. Glide reflection b. Orientation of points c. Parallelism of lines d. Areas of polygons

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What kinds of symmetry do an equilateral and an isosceles triangle have?

An equilateral triangle has six symmetries, and an isosceles triangle has two. An isosceles triangle has a single axis of symmetry, the perpendicular bisector of the non-congruent side. This is a reflection symmetry. An equilateral triangle has rotational symmetry as well as reflection symmetry. It is invariant under rotations by 120 degrees.


How can you show that the spacetime interval is invariant under Lorentz transformations?

One way to show that the spacetime interval is invariant under Lorentz transformations is by using the Lorentz transformation equations to calculate the interval in one frame of reference, and then transforming to another frame of reference using the same equations. If the interval remains the same in both frames, it demonstrates that the spacetime interval is invariant under Lorentz transformations.


How do you find the invariant line of a stretch?

To find the invariant line of a stretch, identify the direction in which the stretch occurs. The invariant line is typically the line that remains unchanged during the transformation, often along the axis of the stretch. For example, if stretching occurs along the x-axis, the invariant line would be the y-axis (or any line parallel to it). You can confirm this by observing that points on the invariant line do not change their position under the stretch transformation.


What are the invariant points of a dilation?

Invariant points of a dilation are the points that remain unchanged under the transformation. In a dilation centered at a point ( C ) with a scale factor ( k ), the invariant point is typically the center ( C ) itself. This means that when a point is dilated with respect to ( C ), it either moves closer to or further away from ( C ), but ( C ) does not move. Therefore, the only invariant point in a dilation is the center of dilation.


What is invariant property?

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Is an air capacitor a time invariant and passive component?

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What happens to the invariant quantities in special relativity?

It depends on what these invariant quantities are. It is not enough to specify that something is invariant, you also need to specify under which operation these quantities do not change (= are invariant). In special relativity there is an operation called a Lorentz transformation which applies the effects of a speed increase, thus applying time dilatation and length contraction. A Lorentz invariant quantity is a quantity which remains the same under this transformation, i.e. it has the same value for every observer in an inertial frame. Examples of such invariants are the lengths of four-vectors, the generalizations of the common 3-dimensional vectors such as those indicating place and momentum. For example the 3d-vector for location (x,y,z) is joined with another quantity for the time dimension into a 4-vector whose length is Lorentz invariant. There are more Lorentz invariant quantities, some of them quite complex.


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What has the author George Wilber Hartwell written?

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