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There is four quantum numbers that are used to describe completely the movement and trajectories of each electron within an atom.

**Principal****Azimuthal****Magnetic****Spin**

*photo owner: ThoughCo*

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In mathematics, a *matrix *(plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in **rows** and **columns.**

- The size of a matrix is defined by the number of rows and columns that it contains. A matrix with
and*m*rowsis called an*n*columns*m*×*n matrix.* - while
*m**n**dimensions*.

The dimensions of the following matrix are 3x3 because there are three rows and three columns.

*N.B: *

*i**describes the number of the row**j**describes the number of the column*

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where P_{ext }is the external pressure, and 🔺V is the change in volume. A classic example of this is a piston. As heat is added to the cylinder, the pressure inside the cylinder increases. The piston then rises to relieve the pressure difference between the pressure inside the cylinder and the external pressure. By increasing the volume in the cylinder, the piston has just done work. Reference the picture below.

The sum of heat and work is the change in internal energy, Δ U .

In an isolated system, q = − w . Therefore, Δ U = 0 .

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