HIGH RESOLUTION OF THE RESOLVE INSTRUMENT ABOARD XARM WILL MAKE IT POSSIBLE THE DETECTION OF INDIVIDUAL EMISSION LINES AND THE MEASUREMENTS OF THEIR PROFILES WITH HIGH ACCURACY ALLOWING THE STUDY OF GAS DYNAMICS IN MANY EXTENDED X-RAY SOURCES INCLUDING GALAXY CLUSTERS GROUPS AND GIANT ELLIPTICAL GALAXIES. MEASURING THE VELOCITIES OF GAS MOTIONS IS ESSENTIAL FOR UNDERSTANDING THE PHYSICS OF RADIO-MODE AGN FEEDBACK THE PARTICLE (RE-)ACCELERATION AND THE ORIGIN OF ENHANCED RADIO EMISSION THE NON-THERMAL PRESSURE SUPPORT AND THE BIAS OF THE HYDROSTATIC MASS MEASUREMENTS. IN ORDER TO ANSWER THESE QUESTIONS IT IS NECESSARY TO DO COMPREHENSIVE STUDIES OF THE VELOCITY FIELD NAMELY TO MEASURE NOT ONLY THE AMPLITUDE OF GAS MOTIONS BUT ALSO THE CHARACTERISTIC SCALES ASSOCIATED WITH THE MOTIONS ANISOTROPY AND STATISTICAL PROPERTIES OF THE VELOCITY FIELD (E.G. VELOCITY POWER SPECTRUM). OUR OBSERVATIONAL PROGRAM DESCRIBED IN SECTION 3 IS TAILORED TO PERFORM SUCH DETAILED STUDIES. DURING THE PV PHASE OBSERVATIONS WE PROPOSE TO FOCUS ON TWO NEARBY GALAXY CLUSTERS: THE PERSEUS CLUSTER WHICH SHOWS STRONG AGN ACTIVITY IN THE CENTER; AND THE COMA CLUSTER - A NON-COOL-CORE CLUSTER WITH UNDERGOING MERGING ACTIVITY. AFTER THE PV PHASE THE DEVELOPED TECHNIQUES WILL BE APPLIED ON A SAMPLE OF CLUSTERS GROUPS AND MASSIVE ELLIPTICAL GALAXIES. IN ORDER TO MEASURE SPATIALLY-RESOLVED AMPLITUDE OF GAS MOTIONS (DISPERSION AND BULK VELOCITIES) WE WILL PRODUCE THE MAPS OF LINE WIDTHS AND VARIATIONS OF LINE CENTROIDS. THE HITOMI OBSERVATORY HAS ALREADY DEMOSTRATED THE FEASIBILITY OF SUCH MEASUREMENTS AND PROVIDED VELOCITY MAPS IN THE INNER _ 100 KPC REGION IN PERSEUS [1]. WE WILL ALSO MEASURE THE VELOCITIES OF GAS MOTIONS USING THE RESONANT SCATTERING EFFECT [10]. BOTH DIAGNOSTICS AS A FUNCTION OF RADIUS DEPEND DIFFERENTLY ON THE DIRECTIONALITY OF GAS MOTIONS. THEREFORE COMPARING THE RESULTS WE WILL BE ABLE TO CONSTRAIN THE ANISOTROPY OF MOTIONS [3 4]. THE FIRST HITOMI OBSERVATIONS CONFIRMED THE THEORETICAL PREDICTIONS OF FLUX SUPPRESSION IN THE STRONGEST HE-LIKE FE LINE IN THE PERSEUS CORE DUE TO THE RESONANT SCATTERING OF PHOTONS. COMPARING THE OBSERVED SUPPRESSION WITH THE RESULTS OF RADIATIVE TRANSFER SIMULATIONS THE VELOCITIES OF GAS MOTIONS HAVE BEEN MEASURED [2]. THE STATISTICAL UNCERTAINTIES ON THE MEASURED LINE FLUXES ARE CURRENTLY TOO LARGE FOR ANISOTROPY STUDIES. HOWEVER THEY CAN BE SIGNIFICANTLY IMPROVED WITH NEW XARM OBSERVATIONS. FINALLY WE PROPOSE TO PROBE VELOCITY POWER SPECTRA THAT PROVIDE INFORMATION ABOUT THE INJECTION SCALE OF MOTIONS AND VELOCITY AMPLITUDE ON EACH SPATIAL SCALE. THE METHODS THAT EXRACT THIS INFORMATION FROM THE OBSERVABLES HAVE BEEN DEVELOPED INITIALLY BY ZHURAVLEVA ET AL. [5] AND THEN FURTHER MODIFIED FOR THE COMA CLUSTER BY ZUHONE ET AL. [6]. THE APPLICATION OF THESE TECHNIQUES REQUIRES MULTIPLE VELOCITY MEASUREMENTS AT DIFFERENT RADII. COMPARISON OF THE MEASURED WITH XARM VELOCITY POWER SPECTRA AND THE INDIRECTLY MEASURED ONES FROM THE CHANDRA IMAGES [7 8] WILL CALIBRATE THE STATISTICAL RELATION BETWEEN THE AMPLITUDE OF DENSITY FLUCTUATIONS AND VELOCITY POWER SPECTRUM PROVIDING AN EFFECTIVE METHOD TO MEASURE VELOCITY POWER SPECTRA IN MANY OBJECTS. IT IS IMPORTANT TO MENTION THAT ANY DIFFERENCES BETWEEN THE DIRECT AND INDIRECT MEASUREMENTS WILL PROVIDE INFORMATION ABOUT THE ELECTRON CONDUCTION GAS VISCOSITY AND THE EFFECTS OF MAGNETIC FIELDS [12]