= Solution
Apply the product from right to left, choosing every <Givens rotation> from the current first column. First $J(1,2)$ replaces $(a_1,a_2)$ by $(\sqrt{a_1^2+a_2^2},0)$. Next $J(1,3)$ combines that retained entry with $a_3$ and sets the third entry to zero. Inductively, after eliminating coordinates $2,\ldots,k$, the first coordinate is
$$
\sqrt{a_1^2+\cdots+a_k^2},
$$
and coordinates $2,\ldots,k$ are zero. Later <Givens rotations> involve only coordinate one and a new coordinate, so those zeros remain zero. Therefore
$$
\boxed{Q_1a=(\|a\|_2,0,\ldots,0)^T=\|a\|_2e_1,}
$$
where $e_1$ is the first <standard basis> <vector>. The zero <vector> is included by choosing the <identity matrix> for every zero pair. The nonnegative sign follows from the convention fixed in part (c)(ii). This is the first-column stage of <QR decomposition by Givens rotations>.
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