  Despite much theoretical effort, there is no complete theory of the 'strange'
metal state of the high temperature superconductors, and its
linear-in-temperature, $T$, resistivity. Recent experiments showing an
unexpected linear-in-field, $B$, magnetoresistivity have deepened the puzzle.
We propose a simple model of itinerant electrons, interacting via random
couplings with electrons localized on a lattice of quantum 'dots' or 'islands'.
This model is solvable in a large-$N$ limit, and can reproduce observed
behavior. The key feature of our model is that the electrons in each quantum
dot are described by a Sachdev-Ye-Kitaev model describing electrons without
quasiparticle excitations. For a particular choice of the interaction between
the itinerant and localized electrons, this model realizes a controlled
description of a diffusive marginal-Fermi liquid (MFL) without momentum
conservation, which has a linear-in-$T$ resistivity and a $T \ln T$ specific
heat as $T\rightarrow 0$. By tuning the strength of this interaction relative
to the bandwidth of the itinerant electrons, we can additionally obtain a
finite-$T$ crossover to a fully incoherent regime that also has a linear-in-$T$
resistivity. We show that the MFL regime has conductivities which scale as a
function of $B/T$; however, its magnetoresistance saturates at large $B$. We
then consider a macroscopically disordered sample with domains of MFLs with
varying densities of electrons. Using an effective-medium approximation, we
obtain a macroscopic electrical resistance that scales linearly in the magnetic
field $B$ applied perpendicular to the plane of the sample, at large $B$. The
resistance also scales linearly in $T$ at small $B$, and as $T f(B/T)$ at
intermediate $B$. We consider implications for recent experiments reporting
linear transverse magnetoresistance in the strange metal phases of the
pnictides and cuprates.
