Step 1 (Nucleophilic substitution with aqueous KOH):
\[
\mathrm{C_2H_5Br + OH^- \;\longrightarrow\; C_2H_5OH + Br^-}
\]
Therefore, \(\boxed{A = \mathrm{C_2H_5OH}\;(\text{ethanol})}\).
Step 2 (Oxidation with acidified K$_2$Cr$_2$O$_7$ under heat):
Under reflux/heat, primary alcohols are oxidised to carboxylic acids.
\[
\mathrm{C_2H_5OH \;+\; [O] \;\xrightarrow[\Delta]{\mathrm{K_2Cr_2O_7/H_2SO_4}}\; CH_3COOH \;+\; H_2O}
\]
Hence, \(\boxed{B = \mathrm{CH_3COOH}\;(\text{ethanoic acid})}\).