<s>
In	O
mathematics	O
,	O
a	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
two	O
dimensions	O
is	O
a	O
mapping	B-Algorithm
from	O
an	O
xy-Cartesian	O
coordinate	O
system	O
to	O
an	O
x′y′-Cartesian	O
coordinate	O
system	O
in	O
which	O
the	O
origin	O
is	O
kept	O
fixed	O
and	O
the	O
x′	O
and	O
y′	O
axes	O
are	O
obtained	O
by	O
rotating	O
the	O
x	O
and	O
y	O
axes	O
counterclockwise	O
through	O
an	O
angle	O
.	O
</s>
<s>
A	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
more	O
than	O
two	O
dimensions	O
is	O
defined	O
similarly	O
.	O
</s>
<s>
A	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
is	O
a	O
linear	B-Architecture
map	I-Architecture
and	O
a	O
rigid	B-Algorithm
transformation	I-Algorithm
.	O
</s>
<s>
which	O
is	O
the	O
standard	O
matrix	O
equation	O
of	O
a	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
in	O
two	O
dimensions	O
.	O
</s>
<s>
Through	O
a	O
change	O
of	O
coordinates	O
(	O
a	O
rotation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
and	O
a	O
translation	B-Algorithm
of	I-Algorithm
axes	I-Algorithm
)	O
,	O
equation	O
(	O
)	O
can	O
be	O
put	O
into	O
a	O
standard	O
form	O
,	O
which	O
is	O
usually	O
easier	O
to	O
work	O
with	O
.	O
</s>
<s>
Generalizing	O
to	O
any	O
finite	O
number	O
of	O
dimensions	O
,	O
a	O
rotation	B-Algorithm
matrix	I-Algorithm
is	O
an	O
orthogonal	B-Algorithm
matrix	I-Algorithm
that	O
differs	O
from	O
the	O
identity	B-Algorithm
matrix	I-Algorithm
in	O
at	O
most	O
four	O
elements	O
.	O
</s>
