\[
    \underline{p}(t)=
    \begin{pmatrix}
       \sin{t}
       \\
       \cos{t}
    \end{pmatrix},
    \qquad
    \underline{q}(t)=
    \begin{pmatrix}
       \cos{t}
       \\
       -\sin{t}
    \end{pmatrix}
\]
Not a RHS:
\[
   \underline{\widehat q}(t)=\underline{p}(t),
   \qquad
   \underline{\widehat p}(t)=-\underline{q}(t)
\]
\[
   \underline{p}'(t)=\underline{q}(t),
   \qquad
   \underline{q}'(t)=-\underline{p}(t)
\]