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The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors are equal to 1, we have directional scaling. In the case where v x = v y = v z = k, scaling increases the area of any surface by a factor of k 2 and the volume of any solid object by a factor of k 3.
Therefore, the shear factor m is the cotangent of the shear angle between the former verticals and the x-axis. (In the example on the right the square is tilted by 30°, so the shear angle is 60°.) (In the example on the right the square is tilted by 30°, so the shear angle is 60°.)
In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. [2] [3] [4] Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific ...
Out of 20 products it tracked from prior to the pandemic until today, about 60% had reduced their sheet count, the study found. (Only one item, a 2-pack of Scott multipurpose shop towels, declined ...
The sum of the entries along the main diagonal (the trace), plus one, equals 4 − 4(x 2 + y 2 + z 2), which is 4w 2. Thus we can write the trace itself as 2w 2 + 2w 2 − 1; and from the previous version of the matrix we see that the diagonal entries themselves have the same form: 2x 2 + 2w 2 − 1, 2y 2 + 2w 2 − 1, and 2z 2 + 2w 2 − 1. So ...
Donald Trump’s siding with Elon Musk over visas for high-tech workers is the most significant example yet of the president-elect favoring powerful elements in his new MAGA coalition over his ...
A joint session of Congress will meet Jan. 6 to count the electoral votes certifying Trump's victory four years after a mob of Trump supporters violently attacked the Capitol in protest of ...
This means that the tape changes length by 1.16 mm per 10 m tape per 10 °C change from the standard temperature of the tape. For a 30 meter long tape with standard temperature of 20 °C used at 40 °C, the change in length is 7 mm over the length of the tape.
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