The change - of - coordinate matrix from mathscr{B} = left{begin{bmatrix}3-14end{bmatrix}begin{bmatrix}20 -5 end{bmatrix}begin{bmatrix}8-27 end{bmatrix}right} to the standard basis in RR^{n}.

This question has to do with binary star systems, where i is the angle of inclination of the system.
Calculate the mean expectation value of the factor ${\displaystyle {\sin }^3}$ i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if ${\displaystyle {\sin }^3}$ i has its mean value.
Hint: In spherical coordinates, ${\displaystyle (\theta ,\varphi )}$, integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by ${\displaystyle \sin \left\{3\right\}\left(\theta \right)}$.
${\displaystyle v_1=100k\frac{m}{s}}$
${\displaystyle v_2=200k\frac{m}{s}}$
Orbital period ${\displaystyle =2}$ days
${\displaystyle M_1=5.74e33g}$
${\displaystyle M_2=2.87e33g}$

Solvin system of equations graphically

Which of the following coordinate systems is most common?
a. rectangular
b. polar
c. cylindrical
d. spherical

Give a full answer for the given question: The covalent backbone of DNA and RNA consists of: ?

What coordinate system is suggested if the integrand of a triple integral involves $x^2+y^2?$

Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed
$a)\overrightarrow{A}(x,y,z)={\overrightarrow{e}}_x$
$d)\overrightarrow{A}(\rho ,\varphi ,z)={\overrightarrow{e}}_{\rho }$
$g)\overrightarrow{A}(r,\theta ,\varphi )={\overrightarrow{e}}_{\theta }$
$j)\overrightarrow{A}(x,y,z)=\frac{-y{\overrightarrow{e}}_x+x{\overrightarrow{e}}_y}{x^2+y^2}$

The Cartesian coordinates of a point are given.
a) ${\displaystyle (2,-2)}$
b) ${\displaystyle (-1,\sqrt{3})}$
Find the polar coordinates ${\displaystyle (r,\theta )}$ of the point, where r is greater than 0 and 0 is less than or equal to ${\displaystyle \theta }$, which is less than ${\displaystyle 2\pi }$
Find the polar coordinates ${\displaystyle (r,\theta )}$ of the point, where r is less than 0 and 0 is less than or equal to ${\displaystyle \theta }$, which is less than ${\displaystyle 2\pi }$