2) Consider the previously defined coordinate systems Fits and F Denote latitude by the symbol A and longitude by the symbol (1)/(2) Measure latitude positive north and negative south of the equator, -900leqslant lambda leqslant +90^circ Measure langitude positive east and negative west of zero longitude -180^circ lt mu leqslant +180^circ (a) Given the latitude A. and longitude A int _(0)^pi find a transformation matrix from F to F_(2)(T_(min )) that is a function only of A. and A. (b) Using your answer to part 2a transform the Earth's rotation vector in F_(C) to its representation in Earth-fixed coordinates at Blacksburg, Vinginla USA (F_(c)=F_(cm)) .That is, transform funday to omega _(m)) Use n_(man)=3712.442m mu _(max)=80-24.446m

(a) To find the transformation matrix from the coordinate system F to , we need to consider the given latitude and longitude coordinates.The latitude is denoted by the symbol A and ranges from -90° to +90°, with positive values indicating north of the equator and negative values indicating south of the equator. The longitude is denoted by the symbol and ranges from -180° to +180°, with positive values indicating east of zero longitude and negative values indicating west of zero longitude.The transformation matrix from F to can be expressed as: This matrix represents a rotation about the z-axis by an angle A (latitude) and a rotation about the y-axis by an angle (longitude).(b) To transform the Earth's rotation vector in to its representation in Earth-fixed coordinates at Blacksburg, Virginia, USA, we need to use the given values for the north-south and east-west components of the rotation vector.The north-south component is given by and the east-west component is given by .Using the transformation matrix from part (a), we can multiply the Earth's rotation vector in by the transformation matrix to obtain the representation in Earth-fixed coordinates: Therefore, the representation of the Earth's rotation vector in Earth-fixed coordinates at Blacksburg, Virginia, USA is: