We have shown that the thermal emission of the amorphous dust composed of amorphous silicate dust (a-Si) and amorphous carbon dust (a-C) provides an excellent fit both to the observed intensity and the polarization spectra of molecular clouds. The anomalous microwave emission (AME) originates from the resonance transition of the two-level systems attributed to the a-C with an almost spherical shape. On the other hand, the observed polarized emission in submillimeter wave bands is coming from a-Si. By taking into account a-C, the model prediction of the polarization fraction of the AME is reduced dramatically. Our model prediction of the 3σ lower limits of the polarization fraction of the Perseus and W 43 molecular clouds at 17 GHz are 8.129 × 10-5 and 8.012 × 10-6, respectively. The temperature dependence of the heat capacity of a-C shows the peculiar behavior compared with that of a-Si. So far, the properties of a-C are unique to interstellar dust grains. Therefore, we coin our dust model as the cosmic amorphous dust model.