= Solution
An invariant has the same value when the same physical event or state is described in different <inertial frames>. A conserved quantity has the same value as the physical system evolves, subject to its equations and isolation conditions. These are different comparisons. The <invariant mass> of a heated object can change with <time>, while an isolated system's conserved <energy> has different numerical values in boosted frames.
Under a <Lorentz transformation> $x'^\mu=\Lambda^\mu{}_{\nu}x^\nu$, a <Lorentz four-vector> transforms as
$$
\boxed{V'^\mu(x')=\Lambda^\mu{}_{\nu}V^\nu(x).}
$$
A <covector> transforms by the inverse matrix, $W'_\mu=(\Lambda^{-1})^\nu{}_{\mu}W_\nu$. A general <tensor> has one corresponding factor for each index; for example,
$$
\boxed{T'^{\mu\nu}{}_{\rho}(x')=
\Lambda^\mu{}_{\alpha}\Lambda^\nu{}_{\beta}
(\Lambda^{-1})^\gamma{}_{\rho}T^{\alpha\beta}{}_{\gamma}(x).}
$$
Contraction with the <Minkowski metric> produces <Lorentz scalars>; it does not by itself make those scalars conserved.
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