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We study the generalized quadratic Gaussian CEO problem where K jointly Gaussian remote sources are transformed and independently-Gaussian-corrupted to form L observations, which are separately compressed by L encoders while the decoder attempts to reconstruct the K remote sources subject to a sum-distortion constraint. We first give a sufficient condition for the existing inner and outer regions to coincide, and then show that the new condition contains more matching cases than Oohama's. The main novelty lies in the fact that rotating the remote sources via orthogonal transformation while keeping a constant observation covariance matrix and the same observation noises does not change the rate region. Further, by exploiting the relationship between the sum-rate bound of the generalized quadratic Gaussian CEO problem and that of the quadratic Gaussian multiterminal source coding problem, we obtain new cases of the latter with tight sum-rate bound.