Let \( f(r, \theta)=(r \cos \theta, r \sin \theta) \) for \( (r, \theta) \in R^{?} \) with \( r \neq 0 \).
Which of the following statements are correct?
(Here DS denotes the derivative of \( f \) ).
1. the linear transformation \( D f(r, \theta) \) is not zero for any \( (r, \theta) \in \mathbb{R}^{2} \) with \( r \neq 0 \)
2. \( f \) is one-one on \( \left\{(r, \theta) \in R^{2}: r \neq 0\right\} \)
3. for any \( (r, \theta) \in \mathbb{R}^{2} \) with \( r \neq 0 . f \) is one-one on a neighborhood of \( (r, \theta) \)
4. Df \( (r, \theta)=r^{2} l \) for any \( (r, \theta) \in R^{2} \) with \( r \neq 0 \)
