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If we rotate basis vectors i' and j' by angle
from i and j, (so that the i' direction rotates toward j) the components
of a fixed vector v change as follows:
vi becomes
vi' = vi cos
+ vj sin
and vj becomes
vj' = - vi sin
+ vj cos
These effects are illustrated in the accompanying applet. You can move the vectors and also rotate the basis.
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