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  2. Section modulus - Wikipedia

    en.wikipedia.org/wiki/Section_modulus

    y C, y T are the distances from the PNA to their centroids. Plastic section modulus and elastic section modulus can be related by a shape factor k: = = This is an indication of a section's capacity beyond the yield strength of material. The shape factor for a rectangular section is 1.5. [1]

  3. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    The old coordinates (x, y, z) of a point Q are related to its new coordinates (x′, y′, z′) by [14] [′ ′ ′] = [⁡ ⁡ ⁡ ⁡] []. Generalizing to any finite number of dimensions, a rotation matrix A {\displaystyle A} is an orthogonal matrix that differs from the identity matrix in at most four elements.

  4. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    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 ...

  5. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    If a = 0 and b ≠ 0, the line is horizontal and has equation y = -c/b. The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 - (-c/b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as ...

  6. List of electromagnetism equations - Wikipedia

    en.wikipedia.org/wiki/List_of_electromagnetism...

    Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.

  7. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Here the coefficient A is the amplitude, x 0, y 0 is the center, and σ x, σ y are the x and y spreads of the blob. The figure on the right was created using A = 1, x 0 = 0, y 0 = 0, σ x = σ y = 1.

  8. Partition function (statistical mechanics) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    This dependence on microscopic variables is the central point of statistical mechanics. With a model of the microscopic constituents of a system, one can calculate the microstate energies, and thus the partition function, which will then allow us to calculate all the other thermodynamic properties of the system.

  9. Law of total covariance - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_covariance

    Note: The conditional expected values E( X | Z) and E( Y | Z) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z) is g(Z). Similar comments apply to the conditional covariance.