If we rotate basis vectors
$\widehat{i\text{'}}$ and
$\widehat{j\text{'}}$ by angle
$\theta $ from
$\widehat{i}$ and
$\widehat{j}$, (so that the
$\widehat{i\text{'}}$ direction rotates toward
$\widehat{j}$ )
the components of a fixed vector
$\stackrel{\u27f6}{v}$
change as follows: