  Several new $q$-supercongruences are obtained using transformation formulas
for basic hypergeometric series, together with various techniques such as
suitably combining terms, and creative microscoping, a method recently
developed by the first author in collaboration with Wadim Zudilin. More
concretely, the results in this paper include $q$-analogues of supercongruences
(referring to $p$-adic identities remaining valid for some higher power of $p$)
established by Long, by Long and Ramakrishna, and several other
$q$-supercongruences. The six basic hypergeometric transformation formulas
which are made use of are Watson's transformation, a quadratic transformation
of Rahman, a cubic transformation of Gasper and Rahman, a quartic
transformation of Gasper and Rahman, a double series transformation of Ismail,
Rahman and Suslov, and a new transformation formula for a nonterminating
very-well-poised ${}_{12}\phi_{11}$ series. Also, the nonterminating $q$-Dixon
summation formula is used. A special case of the new ${}_{12}\phi_{11}$
transformation formula is further utilized to obtain a generalization of
Rogers' linearization formula for the continuous $q$-ultraspherical
polynomials.

Number Theory;Combinatorics