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Using a simple two-color selection based on $g$-, $z$-, and $K$-bandphotometry, we pick out 1609 star-forming galaxies (sgzKs) and 422 passivelyevolving galaxies (pgzKs) at z\sim2$ from a $K$-band-selected sample ($K_{\rmAB} < 22.0$) in an area of $\sim 0.44$ deg$^{2}$ of the All-wavelength ExtendedGroth Strip International Survey. The number counts of pgzKs\ in our sampleturn over at $K_{\rm AB} \sim 21.0$, and both the number of faint and brightobjects (including sgzKs\ and pgzKs) exceed the predictions of a recentsemi-analytic model of galaxy formation, a more successful model is need toexplain this diversity. We also find that the star formation rate (SFR) andspecific SFR (sSFR) of sgzKs\ increases with redshift at all masses, implyingthat star-forming galaxies were much more active on average in the past.Moreover, the sSFR of massive galaxies is lower at all redshifts, suggestingthat star formation contributes more to the mass growth of low-mass galaxiesthan to high-mass galaxies. From {\it Hubble Space Telescope} Wide Field Camera3 near-infrared imaging data, we find that morphologies of $z\sim2$ galaxiesnot only have diffuse structures with lower $G$ and higher $M_{20}$ values, butalso have single-object morphologies (higher $G$ and lower $M_{20}$), implyingthat there are morphological variety and different formation process for thesegalaxies at $z\sim2$. Finally, we also study the fraction of active galacticnuclei (AGNs) in the gzKs, 82 of 828 gzKs\ with four IRAC bands can beclassified as AGNs ($\sim$ 10%). Most of these AGN candidates have $L_{\rm0.5-10\ keV}>10^{41}\,\rm erg\,s^{-1}$.

Passive and star-forming galaxies at $1.4 \leq z \leq2.5$ in the Aegis field