Question

If the original coordinate axes are rotated 30° to obtain the x' and y' axes, what is the value of x in terms of x' and y'?

Answer 1

\[x=\sqrt{\frac{ 3 }{ 2}}x'-\frac{ 1 }{ 2}y'\]

Answer 2

\[x=\sqrt{\frac{ 3 }{ 2}}x'+\frac{ 1 }{ 2}y'\]

Answer 3

x=\\frac{ 1 }{ 2}}x'-\[x=\frac{ 1 }{ 2}x'-\sqrt{\frac{ 3 }{ 2}}y'\]\frac{ 1 }{ 2}y'

Answer 4

\[x=\frac{ 1}{ 2}x'+\sqrt \frac{ 3 }{ 2}y'\]

Answer 5

a
b
c
d

Answer 6

@Michele_Laino

Answer 7

@dan815

Answer 8

here we can compute the (2x2) matrix N such that the subsequent equation holds:
\[\left( {\begin{array}{*{20}{c}}
{x'} \\
{y'}
\end{array}} \right) = N\left( {\begin{array}{*{20}{c}}
x \\
y
\end{array}} \right)\]