Understanding how tasks are processed across the entire brain is a central yet complex question in neuroscience. Recently, the release of brainwide electrophysiological recordings in a standardized behavior task offers an unprecedented opportunity to approach this question. In this paper, we characterize the signal activity of all the cortical regions systematically, and correlate the resulting functional properties with their corresponding anatomical positions. Taking advantage of the proposed brainwide reduced-rank regression encoding model that is unified and well-performing, we measured two properties of the task-driven activity (timescale and dimensionality) and two properties of the selectivity (overall modulation and variable-specific selectivity) for each cortical region separately. Task-driven activity-wise, we found that as the signal gets more processed (i.e., as the brain region moving up along the anatomical hierarchy from the Allen Mouse Brain Connectivity Atlas), the signal becomes significantly slower in fluctuation and lower in dimensionality. Selectivity-wise, we made two observations: first, when considering the effect of all the variables combined, regions in the frontal area are significantly more modulated by the task than those in the sensory area; second, when considering the effect of each variable individually, the brain is structured categorically, with visual, somatosensory, and frontal areas exhibiting distinct selectivity profiles. Overall, exploiting the unified encoding model and brainwide IBL dataset, our study revealed several intimate relationships between the functional properties of cortical regions and their anatomical positions.