how to write that equition?

[gantsooj]

please help for write following equition!!

ve = |ve| * (cos(w)*t  -sin(w)*t)
            (sin(w)*t  cos(w)*t)   * vk / |vk|

cos -sin
sin cos
they are within one ( )

i think that
*((cos - sin) / (sin + cos))*
is it right?

[tition]

Almost certainly it isn't: in the formula you wrote,

(cos(w)*t  -sin(w)*t)
(sin(w)*t   cos(w)*t) 

is a matrix (in fact it should be written with two big brackets on the left and on the right). You cannot realize that formula as *((cos - sin) / (sin + cos))*. If you want to learn more on matrices, you can read

http://en.wikipedia.org/wiki/Matrix_(mathematics)

If you want to learn how to write complex numbers in matrix form (which is done via the matrix you typed) you can read

http://en.wikipedia.org/wiki/Complex_number

[gantsooj]

yeah, but i don't undertsand that there're 4 matrix elements within big bracket and multiple the somevalue. then the result must have matrix with 4 elements. but in the equition is value v_e = . it means take just one value not matrix.
here |v_e| is estimated translational speed
matrix is a rotational velocity,
v_k is a translational velocity.
result v_e is velocity